To find the starting amounts of cranberry and orange punch, we equate 2/3 of the cranberry punch to 5/6 of the orange punch. After setting up the equation 2/3 * C = 5/6 * O, we can solve for either C or O given a specific amount for one.
Explanation:Understanding Proportional Quantities in Punch
To determine how many ounces of cranberry and orange punch might have been at the start of the party, given that guests drank 2/3 of the cranberry punch and 5/6 of the orange punch, and that they drank the same amount of each, we can set up an equation. Let's label the amount of cranberry punch initially as C ounces and the amount of orange punch initially as O ounces. According to the problem, 2/3 of C is equal to 5/6 of O; therefore:
2/3 * C = 5/6 * O
We can find a common multiple of the denominators 3 and 6 to solve the equation. For simplicity, let's assume that the common multiple is 6. If we multiply both sides of the equation by 6 to get rid of the fractions, we have:
4 * C = 5 * O
This means that the amount of cranberry punch is always 5/4 times the amount of orange punch. For example, if there were 20 ounces of orange punch at the start (O = 20), then there would have been 5/4 * 20 = 25 ounces of cranberry punch (C).
Final answer:
The party guests drank equal amounts of 2/3 of cranberry punch and 5/6 of orange punch. By setting up an equation and choosing a common multiple of the denominators (6), we conclude that one possible starting amount for each type of punch is 18 ounces, demonstrating that whenever x is chosen, y will be equal to x.
Explanation:
The student's question involves solving a problem where two quantities are compared to find out how much of each was present initially. Since the guests drank the same amount of cranberry punch and orange punch, with the proportions being 2/3 and 5/6 respectively, we can set up an equation to solve for the initial amounts.
Let x represent the original amount of cranberry punch and y represent the original amount of orange punch. According to the question:
2/3 of cranberry punch = 5/6 of orange punch
(2/3)x = (5/6)yTo find multiple answers, we could assume a common multiple of both denominators 3 and 6, which is 6. Then, if we let x = 6 and y = 6, we have:
(2/3)×6 = 4(5/6)×6 = 5However, these amounts are not equal. We need to find a value for x and y that, when substituted into the proportion, yields an equal amount for both types of punch. Multiply both sides of the equation by 3/2 to isolate y:
y = (3/2) × (2/3)xy = xNow, we can select any multiple of 6 for x to represent the initial amount. If we choose multiple of 6 such as 18 ounces for x, then y would also be 18 ounces. Thus, the starting amount of both cranberry punch and orange punch could have been 18 ounces each as one of the possible answers.
I need help with this question 2 -3/4K=1/8k+9
The value of k in the expression is -8.
We have,
2 - (3/4)k = (1/8)k + 9
Combine like terms on one side.
-(3/4)k - (1/8)k = 9 - 2
Simplify.
-k (3/4 + 1/8) = 7
-k (6 + 1)/8 = 7
-(7/8)k = 7
Multiply 8 on both sides.
-(7/8)k x 8 = 8 x 7
-7k = 56
Divide -7 on both sides.
k = -56/7
k = -8
Thus,
The value of k in the expression is -8.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ6
Krista's softball team played 35 games this season and lost only 7 of them.
What percent of their games did Krista's team lose?
The fraction [tex]\frac{7}{35}[/tex] represents how many games Krista's softball team lost out of the 35 games Krista's team played.
To find the percent of games that Krista's team lost, we need to turn the fraction [tex]\frac{7}{35}[/tex] into a percent.
We can reduce [tex]\frac{7}{35}[/tex] by dividing both the numerator and denominator by the Greatest Common Factor of 7 and 35 using 7.
7 ÷ 7 = 1
35 ÷ 7 = 5
Now, we have our reduced fraction.
1 ÷ 5 = 0.2
0.2 × 100 = 20%
Therefore, Krista's softball team lost 20% of their games.
There are 20 balls in a bag. Ten of the balls are red, 4 are green, and the rest are yellow.
Which ratio represents the number of yellow balls to red balls?
1:5
3:10
2:5
3:5
Answer
Find out the ratio represented the number of yellow balls to red balls .
To proof
Let us assume that the number of yellow balls be x.
As given
There are 20 balls in a bag.
Ten of the balls are red, 4 are green, and the rest are yellow.
than the equation becomes
x + 10 + 4 = 20
x = 20 - 14
x = 6
therefore the number of yellow balls be 6 .
Now find out the ratio between the the number of yellow balls to red balls .
the number of yellow balls be 6 .
the number of red balls be 10 .
[tex]\frac{Number\ of\ yellow\ balls}{Number\ of\ red\ balls} = \frac{6}{10}[/tex]
solving
[tex]\frac{Number\ of\ yellow\ balls}{Number\ of\ red\ balls} = \frac{3}{5}[/tex]
Therefore the ratio of the the number of yellow balls to red balls is 3 :5 .
Option (d) is correct .
Hence proved
Write a true proportion from each set of four numbers. Is it possible to make another proportion using the same set of numbers?
4.5; 6; 9; 12
Please help!!! It's about the types of quantities if they are proportional or not if there is a constant number.
Jim and Holly are making gingerbread men. It takes them both 2 minutes to make 2 gingerbread shapes. At this rate, how many people are needed to make 400 gingerbread men in 400 minutes?
Which operation should you perform first when you simplify 175 - (8 + 45 / 3) * 7? A. Addition B. Division C. Multiplication D. Subtraction
PLEASE ANSWER THIS IM IN A HURRY
Answer:
B. Division
Step-by-step explanation:
We have been given an expression [tex]175-(8+\frac{45}{3})*7[/tex]. We are asked to determine which operation will we use first to simplify our given expression.
Using order of operations PEMDAS, we will remove parenthesis first. To remove parenthesis, we need to simplify [tex]\frac{45}{3}[/tex].
Therefore, we will use division first to simplify our given expression.
britney found a swimsuit that she wanted to buy with a pricetag of $80 the sign above it indicated that this price was 20% off. what was the original price of the swimsuit
How do you divide 100.5/1.5
The theoretical time for an apple to drop 2 meter is 0.64 second.sam did the experiment himself and measured that it took 0.62 second for him. What is the percent error?
Explain why 3(5x) is not equivalent to (3*5)(3*x).
sally is x years old and her sister ann is 4years younger. If the product of their ages is 140, form an equation in x and solve it to find ann's age
the fastest ball game in the world may well be Jai-Alai. In it, players use to scoop attached to their hand to throw a small hard ball as fast as 188 mph at an granite wall. To the nearest tenth of a kilometer, about how fast is that speed in km/h
Step-by-step explanation:
Speed with which the players throw a small hard ball is 188 miles per hour. We need to convert the speed of the ball in kilometers per hour.
Firstly we can see the conversion from mile per hour to kilometer per hour as :
1 miles = 1609.34 meters
Also, 1 mile per hour = 1.60934 kilometer per hour
To convert 188 mph to km/h we can use the unitary method as :
188 mile per hour = 1.60934 × 188 kilometer per hour
188 mile per hour = 302.557 kilometer per hour
So, the speed of the ball is 188 miles per hour or 302.557 kilometer per hour. Hence, this is the required solution.
PLEASE HELP ME I WILL DO ANYTHING I NEED HELP ASAP PLEASE HELP ME
A rock climber descends from a peak at a rate of 1/20 vertical km each minute. What is the climber's total change in elevation in 10/11 min?
Enter your answer in the box as a simplified fraction.
The cost of 9 oranges is $1. What is the cost of 3 dozen oranges?
a dozen is 12
Answer:
$4
Step-by-step explanation:
36/9=4
36 is the number of oranges.
We know that 9 oranges is $1.
If 36 goes into 9, 4 times, that means 36 oranges costs $4.
Hope this helps :)
what does the variable, K, stand for in this problem, 2+ 5.3K= 18.43
Suppose you are driving to visit a friend in another state. You are driving at an average rate of 50 miles per hour. You must drive a total of 345 miles. If you have already driven 145 miles, how long will it take you to reach your destination?
To calculate the remaining travel time to reach a destination, subtract the distance already driven from the total trip distance, then divide the remaining distance by the average speed. For this question, after driving 145 miles out of 345, and traveling at an average speed of 50 miles per hour, it will take 4 more hours to reach the destination.
Explanation:The student's question involves calculating the remaining time needed to reach a destination when driving at a constant speed, a typical problem in motion related to average speed and distance. We are given that the total distance is 345 miles, the average speed is 50 miles per hour, and the student has already driven 145 miles. To find the remaining time, we subtract the distance already covered from the total distance and then divide by the average speed.
First, we calculate the remaining distance to be covered by subtracting the distance already driven from the total distance: 345 miles - 145 miles = 200 miles. Next, we determine the time it would take to travel the remaining 200 miles at the average speed of 50 miles per hour. Time is calculated by dividing the remaining distance by the average speed.
Using the formula Time = Distance ÷ Speed, we have Time = 200 miles ÷ 50 miles/hour. This simplifies to 4 hours. Therefore, it will take 4 more hours for the student to reach their destination if they continue to drive at the same average rate of speed.
It will take 4 additional hours to reach the destination by driving the remaining 200 miles at an average speed of 50 miles per hour.
Explanation:To calculate the time it will take to reach the destination, we can use the formula for time which is:
Time = Distance / Speed.
You have already driven 145 miles, so you have 345 miles - 145 miles = 200 miles left to travel. Given that you are driving at an average rate of 50 miles per hour, the remaining travel time can be calculated as follows:
Time = 200 miles / 50 miles per hour = 4 hours.
Therefore, it will take 4 more hours to reach your destination.
To find the time it will take to reach your destination, you need to divide the remaining distance by the average speed. So, if you have already driven 145 miles, you have 345 - 145 = 200 miles left to drive. Using the formula: time = distance / speed, the time it will take to reach your destination is 200 miles / 50 miles per hour = 4 hours.
does the equation y = 20x + 500 represent a linear function
40 is 50% of what number
what is the constant proportionality of 1/3
Final answer:
The constant of proportionality of 1/3 means that for every unit increase in one variable, the other variable increases by 1/3 of that unit. It is a number that relates two quantities that are directly proportional to each other.
Explanation:
The question 'what is the constant of proportionality of 1/3' can be related to various contexts in Mathematics and Science. In mathematics, a constant of proportionality is a number that relates two quantities that are proportional to each other. If one quantity is always the product of the other quantity and a constant, this constant is called the constant of proportionality.
For example, if you have an equation y = (1/3)x, then the constant of proportionality between x and y is 1/3. This means for every unit increase in x, y increases by 1/3 of that unit. It can also appear in a science context, such as in Ohm's Law, where V = IR, and 'R' can be considered the constant of proportionality that relates voltage (V) and current (I), or in the specific heat equation, where the specific heat serves as the constant.
Melinda and Marcus each have a job. Melinda earns $12 an hour. She also receives a $75 weekly bonus.
Melinda made a table to show how much she earns in a given week.
Hours 0 5 10 15 20 25 30 35 40
Weekly Earnings 75 135 195 255 315 375 435 495 555
Marcus earns $15 an hour.
Marcus wrote an equation to determine how much he earns for a given number of hours in a given week.
y=15x
After working a certain number of hours, Melinda and Marcus will have each earned the same amount of money. How much money will they have earned then?
$______
Step by step HELP I HAVE A BAD GRADE IN THIS CLASSSS HELPP
Find the X and Y intercepts of -8x +4y =24
The X and Y intercepts of the given equation can be found by setting variables to zero in turn and solving for the other. The X intercept is -3 and the Y intercept is 6.
Explanation:To find the X and Y intercepts of -8x + 4y =24, we should set each variable equal to zero in turn to solve for the other. The X intercept occurs when Y is zero, and the Y intercept happens where X is zero.
For finding X-intercept, place Y equal to zero in the equation, so we get -8x +4(0) = 24. Solving it leads us to X = -3.
For the Y-intercept, let’s place X equal to zero in the equation. Here we get -8(0) + 4y = 24. Solving this yields Y = 6. So, the X intercept is -3, and the Y intercept is 6.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ2
What is the equation graphed in this figure?
Write a description of how a diagram can help you solve 2x40
Answer: 2 x 40 = 80
Step-by-step explanation: there are two baskets of apple fruit labelled basket X and basket Y, each basket consists 150 green apple fruit.
You were asked to select 40 green apple fruit from each of the basket and put it together in basket Z.
40 green apples from both baskets X and Y equals 80 green apples in basket Z.
2 x 40 =80
Convert 1.580 hectoliters to deciliters.
Mike paid 12 dollars for 3 hamburgers how much does each hamburger cost
Ms.Sim traveled to 42 countries in 60 days.At this rate,how many countries would he travel to in 40 days?
Please help me with my math homework
Write a real world problem that can be represented by the expression 5x + 10
A real world problem reflected in the expression 5x + 10 can involve calculating the total cost of books plus a membership fee in a bookstore. The quadratic formula is used for solving quadratic equations, which have significant applications in various fields.
Explanation:An example of a real world problem represented by the expression 5x + 10 is calculating the total cost of purchasing multiple items. Imagine you are at a bookstore, and each book costs $5. There is also a one-time membership fee to join the bookstore's readers club, which is $10. If x represents the number of books you decide to purchase, then 5x would represent the total cost of the books, and when you add the $10 membership fee, the expression for calculating your total cost would be 5x + 10.
Additionally, the concept of quadratic formula is significant in mathematics as it helps in finding solutions for quadratic equations, such as t² + 10t - 2000 = 0. This equation can be solved by rearranging to have 0 on one side and then applying the quadratic formula. Understanding quadratic equations is crucial not just in theoretical math but also practical real world applications like physics or economics.