a. The lowest total number of cars is ( x = 3 ) Fiats and ( y = 7 ) Rolls Royces, totaling 10 cars.
b. the cheapest solution is to use 3 Fiats and 7 Rolls Royces, costing £240.
To solve this problem, we need to use a system of linear equations and optimization techniques.
Let's define ( x ) as the number of Fiats and ( y ) as the number of Rolls Royces.
The constraints are:
1. People constraint: [tex]\( 2x + 2y \geq 20 \)[/tex] (at least 20 people)
2. Sheep constraint: [tex]\( x + 4y \geq 32 \)[/tex] (at least 32 sheep)
3. Car constraint: [tex]\( x + y \leq 15 \)[/tex] (no more than 15 cars)
We also want to minimize the total number of cars, so the objective function is simply ( x + y ).
(a) To find the lowest total number of cars, we'll solve the system of equations:
[tex]\[\begin{cases}2x + 2y \geq 20 \\x + 4y \geq 32 \\x + y \leq 15\end{cases}\][/tex]
We solve these inequalities by algebraically:
1. Solve the first two equations simultaneously:
[tex]\[ \begin{cases} 2x + 2y = 20 \\ x + 4y = 32 \end{cases} \][/tex]
Multiply the second equation by 2 to match coefficients with the first equation:
[tex]\[ \begin{cases} 2x + 2y = 20 \\ 2x + 8y = 64 \end{cases} \][/tex]
Subtract the first equation from the second:
[tex]\[ \begin{aligned} (2x + 8y) - (2x + 2y) &= 64 - 20 \\ 6y &= 44 \\ y &= \frac{44}{6} \\ y &= 7.33 \end{aligned} \][/tex]
However, ( y ) must be a whole number, so we take ( y = 7).
Substitute ( y = 7 ) into the first equation:
[tex]\[ \begin{aligned} 2x + 2(7) &= 20 \\ 2x + 14 &= 20 \\ 2x &= 6 \\ x &= 3 \end{aligned} \][/tex]
Therefore, the lowest total number of cars is ( x = 3 ) Fiats and ( y = 7 ) Rolls Royces, totaling 10 cars.
(b) To find the cheapest solution, we calculate the cost for each option:
Cost of Fiats: £10 x 3 = £30
Cost of Rolls Royces: £30 x 7 = £210
Total cost: £30 + £210 = £240
So, the cheapest solution is to use 3 Fiats and 7 Rolls Royces, costing £240.
Complete Question:
A farmer has to transport 20 people and 32 sheep to a market. He can use either Fiats (x) which take 2 people and 1 sheep, or Rolls Royces ( y) which take 2 people and 4 sheep. He must not use more than 15 cars altogether.
(a) What is the lowest total numbers of cars he could use?
(b) If it costs £10 to hire each Fiat and £30 for each Rolls Royce, what is the cheapest solution?
Can I get help simplifying these three questions? Thanks!
First Question 3a–a+18–a
Second Question (a+3)–(a+2)
Third Question 43+a–2a
Which phrase could be represented by this expression?
k/5 + 8
or
k over 5 + 8
eight more than a fifth of a number
five times a number plus eight
eight more than five times a number
one-fifth of the sum of a number and eight
If 45 cookies will serve 15 students, how many collies are needed for 30 students?
An interior decorator purchased a painting for $95, a sofa for $225, a chair for $275, and an end table for $155. The tax was $60 and delivery was $75. If she paid for the furniture with $50 bills, how many bills were needed?
42-24 divide 6 ; value 3
The result of the expression 42-24 divided by 6, calculated using the 'Order of Operations' rule, is 38.
Explanation:You've asked to solve this mathematical expression: 42-24 divided by 6. To do this correctly, we must follow the 'Order of Operations,' often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In your problem, the operations are Subtraction and Division. Following the PEMDAS rule, we perform Division before Subtraction. Therefore, first perform 24 divided by 6, which is 4. Then, subtract that result from 42. In the end, 42 minus 4 gives us 38 as the final answer.
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What is the answer to this? I don’t
list all the possible numbers:
10 - cant be divisible by 0
11 - can be divided by 1 and 1
12 - can be divided by 1 and 2
13 - cant be divided by 3
14 - cant be divided by 4
15 - can be divided by 1 and 5
16 - cant be divided by 6
17 - cant be divided by 7
18 - cant be divided by 8
19 - cant be divided by 9
20 - cant be divided by 0
21 - cant be divided by 2
22 can be divided by 2 and 2
23 - cant be divided by 3
24 - can be divided by 2 and 4
the numbers are 11, 12, 15, 22 and 24
58 1/3 ÷ 6 2/3 equals what?
to rent a car,the fast company charges $75 per day plus $0.05 per mile. how many miles did mrs.kline drive if the cost of renting the car was $ 92.40?
Liz earns a salary of $2,100 per month, plus a commission of 5% of her sales. She wants to earn at least $2,400 this month. Write an inequality to find the amount of sales that will meet her goal. Identify what your variable represents.
It costs $2.55 to make a sandwich at the local deli shop. To make a profit, the deli sells it at a price that is 140% of the cost. The sandwich sells for $___.
Use the distributive property of multiplication to find 7 x 22
Hint: 22 = 20 +2
Please show all work, Thank you:)
The distributive property of multiplication is used to simplify 7 x 22. By substituting 22 with 20 + 2 and distributing the multiplication, it becomes 7 x 20 plus 7 x 2, which equals 154.
Explanation:The question is asking us to use the distributive property of multiplication to calculate 7 x 22. The distributive property allows us to multiply a single term and two or more terms inside a set of parenthesis. Here we are given the hint that 22 = 20 + 2.
Following the hint, we substitute 22 with (20 + 2) in the multiplication expression. So, 7 x 22 becomes 7 x (20 + 2). Now, by distributive property, we can take the multiplication inside the parenthesis.
7 x 20 = 140 7 x 2 = 14
By adding both these results, 140 + 14, we get the final answer 154.
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Evaluate the expression 3(7 + 4)2 − 14 ÷ 7. 50 361 363 586
Purple paint is made with a 16:3:1 ratio of white paint:blue paint:red paint. How much white paint, in gallons, is needed in order to make one gallon of purple paint? Express your answer as a common fraction.
Answer:
4/5
Step-by-step explanation:
The purple paint is split into 16+3+1=20 parts: 16 parts of white, 3 parts of blue, and 1 part of red. Thus, in one gallon of purple paint, 16 out of the total 20 parts are white paint, so there are 16/20 x 1 gallon = 4/5 gallons of white paint in one gallon of purple paint.
The amount of white paint that is needed in order to make a gallon of purple paint would be 4 / 5 gallons.
How to find the number of gallons ?The ratio of white:blue:red paint is given as 16:3:1. The sum of these ratio components gives the total parts for one 'unit' of paint.
So, 16 (for white) + 3 (for blue) + 1 (for red) = 20 total parts.
This implies that the 20 parts in this ratio make up 1 gallon of purple paint (as per the question). To find the quantity of white paint needed, we simply need to convert the 'parts' of white paint into gallons.
Since 20 parts is equivalent to 1 gallon, 1 part would be equivalent to 1/20 of a gallon. Therefore, 16 parts of white paint would be equivalent to :
= 16 * (1/20)
= 16/20
= 4/5 gallons
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Help me please 2. You learn from your science teacher that water expands when you freeze it. The next time that you freeze your water bottle, you leave room for the water to expand so that the bottle does not crack. What kind of reasoning did you use? inductive reasoning deductive reasoning algebraic reasoning direct reasoning I think the answer is b
Due to fire laws, no more than 720 people may attend a performance at Metro Auditorium. The balcony holds 120 people. There are 32 rows in the ground floor each for the same number of seats write an inequality to find the numbers of people that can sit in a ground floor row if the balcony is full. Identify what your variable represents.
You buy a movie for 19.99 and a set of earphones for 12.49 how much is the bill before taxes
Answer:32.39
Step-by-step explanation: cost of movie is 19.9
Cost of earphone is 12.49
Adding both cost is 19.9+12.49
=32.39
The cost before tax deduction is 32.39
Which equivalent fraction would you have to use in order to add 3/5 to 21/25
How can the difference 13-(-24)be rewritten as a sum with the correct solution? Explain?
A: (-13) + (-24) = -37
B: 13 + (-24) = -11
C: (-13) + 24 = 11
D: 13 + 24 = 37
Graph y=−56x−4 .
Use the line tool and select two points on the line.
The two points on the line y = − 56x − 4 will be (1, −60) and (−1, 52).
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
y = − 56x − 4
Let x = 1, the value of y will be
y = − 56 (1) − 4
y = − 56 − 4
y = − 60
Let x = − 1, the value of y will be
y = − 56(−1) − 4
y = 56 − 4
y = 52
The two points on the line y = − 56x − 4 will be (1, −60) and (−1, 52). Then the diagram of the line is given below.
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The three seventh grade classes at Sunview Middle School collected the most boxtops for a school fundraiser. They won a $600 prize to share among them. Mr. Aceves’ class collected 3,760 box tops, Mrs. Baca’s class collected 2,301, and Mr. Canyon’s class collected 1,855. How should they divide the money so that each class gets the same fraction of the prize money as the fraction of the box tops that they collected? Explain your reasoning.
Answer: The share would be approximately $285, $175, $141 respectively.
Step-by-step explanation:
Since we have given that
Number of box tops collected by Mr. Aceves's class = 3760
Number of box tops collected by Mrs. Baca's class = 2301
Number of box tops collected by Mr, Canyon's class = 1855
We first find the ration of box tops of Mr. Aceves, Mrs. Baca and Mr. Canyon respectively:
3760:2301:1855
Total = 3760+2301+1855=7916
Total amount to be share among them as a prize = $600
Mr. Aceves's share is given by
[tex]\dfrac{3760}{7916}\times 600\\\\=284.99\\\\\approx 285[/tex]
Mrs. Baca's share is given by
[tex]\dfrac{2301}{7916}\times 600\\\\=175.08\\\\\approx 175[/tex]
Mr. Canyon's share is given by
[tex]\dfrac{1855}{7916}\times 600\\\\=140.60\\\\\approx 141[/tex]
Hence, the share would be approximately $285, $175, $141 respectively.
-0.3,0.5,0.55,-0.35 in least to greatest
The scale on a map is 2cm = 15miles. Dave measures the distance to the next town at 7cm. How many miles away is the next town?
Answer:
[tex]52.5\ miles[/tex]
Step-by-step explanation:
we know that
The scale on the map is equal to
[tex]\frac{2}{15}\frac{cm}{miles}[/tex]
so
by proportion
Find how many miles are [tex]7\ cm[/tex] on the map
[tex]\frac{2}{15}\frac{cm}{miles}=\frac{7}{x}\frac{cm}{miles}\\ \\x=15*7/2\\ \\x=52.5\ miles[/tex]
A used-car dealer has a vehicle on the lot with a sticker price of $5999. if the dealer markup on used vehicles is 20%, how much did the dealer pay for the car?
Answer:
the correct APEX answer is $4999.17
The cost of car is $4,999.16.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A used-car dealer has a vehicle on the lot with a sticker price of $5999.
Mark up = 20%
let the cost of Car be x.
So, x+ 20% of x = 5999
x + 20/100 x = 5999
x + 0.20 x = 5999
1.2 x= 5999
x = 5999/ 1.2
x = $4,999.16
Hence, the cost of car is $4,999.16.
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could someone help please thx
Three times the smaller of two consecutive EVEN integers IS four less than twice the larger. What are the two integers?
PLEASE HELP ME WITH THIS
The two consecutive even integers are 8 and 10.
Given that, three times the smaller of two consecutive even integers is four less than twice the larger.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let two consecutive even integers be x and x+2.
Now, 3x-4=2(x+2)
⇒ 3x-4=2x+4
⇒ 3x-2x=4+4
⇒ x=8
So, x+2=10
Therefore, the two consecutive even integers are 8 and 10.
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Solve the following system of equations algebraically for all values of x,y and z
x+3y+5z=45
6x-3y+2z=-10
-2x+3y+8z=72
The system of equations x+3y+5z=45, 6x-3y+2z=-10, -2x+3y+8z=72 can be solved algebraically to get the values x=6, y=12, z=-1.
Explanation:First, we can combine the first and the second equations and the first and third equations to cancel out y.
Doing so, we get: x+3y+5z+6x-3y+2z=45-10 and x+3y+5z-2x+3y+8z=45+72
The new equations simplify to 7x+7z=35 and -x+13z=117
Next, we can divide the first new equation by 7 to get x+z=5. Subtract x from both sides to get z=5-x.
Substitute z=5-x into the second equation to find the value of x.
Performing these substitutions gives x=6. Substituting x=6 back into the equation z=5-x gives z=-1.
Finally, we substitute x=6 and z=-1 back into the original equations to solve for y: y=(45-6-5(-1))/3 = 12
So, x=6, y=12, z=-1 are the solutions to the system of equations.
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A baseball weighs 5 ounces and the NY Yankees ordered 3,200 baseballs. How many tons do the baseballs weigh?
Answer:
dont come at me if im wrong but im pretty sure the answer is 1/2 or .5
Step-by-step explanation:
Which fraction expresses 36/80 in lowest terms? Please help me ;D
WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!
describe the relationship between: the domain, relation, and range
Relations are subsets of products A×BA×B where AA is the domain and BB the codomain of the relation.
A function ff is a relation with a special property: for each a∈Aa∈A there is a unique b∈Bb∈B s.t. ⟨a,b⟩∈f⟨a,b⟩∈f.
This unique bb is denoted as f(a)f(a) and the 'range' of function ff is the set {f(a)∣a∈A}⊆B{f(a)∣a∈A}⊆B.
You could also use the notation {b∈B∣∃a∈A[⟨a,b⟩∈f]}{b∈B∣∃a∈A[⟨a,b⟩∈f]}
Applying that on a relation RR it becomes {b∈B∣∃a∈A[⟨a,b⟩∈R]}{b∈B∣∃a∈A[⟨a,b⟩∈R]}
That set can be labeled as the range of relation RR.
Eliza earns $400 per week plus $15 for each new customer she signs up. Let c represent the number of new customers Eliza signs up. Write an expression that shows how much she earns in a week. Then find how much Eliza earns in a week in which she signs up 18 customers.
Answer:
400+ (15c)
$670
Step-by-step explanation:
Eliza earns per week = $400
She earns for each new customer's signs up = $15
Let the number of new customers Eliza signs up = c
The expression that shows her earning in a week will be
400+ (15c)
If the number of customers that signs up = 18
The weekly earning of Eliza will be = 400+(15 × 18)
= 400 + 270
= $670
Eliza's earning in a week would be $670.