Question

A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 225 cars and trucks. Dealership B sells twice as many cars and half as many trucks as the Dealership A, and sells a total of 300 cars and trucks. (4 points) a) An equation for the total cars and trucks for Dealership A: b) An equation for the total cars and trucks for Dealership B: c) How many cars did Dealership A sell? d) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?

Answer 1

[AI-generated answer — Bot GPT 3.5]

a) The equation for the total cars and trucks for Dealership A is:

C + T = 225
b) The equation for the total cars and trucks for Dealership B is:
2C + (1/2)T = 300
c) To find how many cars Dealership A sold, we can substitute the value of T from equation (a) into equation (b):
2C + (1/2)(225 - C) = 300
2C + 112.5 - (1/2)C = 300
(3/2)C = 187.5
C = 125
So, Dealership A sold 125 cars.
d) Dealership B sold half as many trucks as Dealership A, which means T = (1/2)T.
Substituting this into equation (b), we get:
2C + (1/2)(2T) = 300
2C + T = 300
Substituting the value of C from part (c):
2(125) + T = 300
250 + T = 300
T = 50
So, Dealership B sold 50 trucks.

Answer 2

[AI-generated answer — Explain Bot]

a) To find the equation for the total cars and trucks sold by Dealership A, we denote the number of cars sold as "c" and the number of trucks sold as "t." Since the total number of cars and trucks sold by Dealership A is 225, we have the equation:

c + t = 225.

b) To find the equation for the total cars and trucks sold by Dealership B, we use the given information that Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A. Let's use the variables "c'" and "t'" to represent the number of cars and trucks sold by Dealership B. The equation becomes:
c' + t' = 300.

c) To determine how many cars Dealership A sold, we can either solve the equation for c + t = 225 or observe that the question doesn't provide any specific information about the number of trucks sold, which means all 225 vehicles could have been cars. Therefore, Dealership A sold 225 cars.

d) Given that Dealership B sold half as many trucks as Dealership A, we can use the equation derived in part (a) to determine the number of trucks sold by Dealership B. Since dealership A sold 225 cars, we have t = 225 - c. We know t' = t/2 (half as many trucks as dealership A). Substituting the value of t from the equation t = 225 - c into t', we get:
t' = (225 - c)/2.

However, the question asks us to find how many trucks Dealership B sold. So we substitute the known value of c' + t' = 300 into the equation:
c' + (225 - c)/2 = 300.

Now, we can solve this equation for c' to find the number of cars sold by Dealership B and then determine the number of trucks sold by subtracting that value from 300 - c'.

Answer 3

[AI-generated answer — Step-by-Step Bot]

a) Let's denote the number of cars sold by Dealership A as "C" and the number of trucks sold as "T". The equation for the total cars and trucks for Dealership A can be written as:

C + T = 225

b) For Dealership B, it is given that it sells twice as many cars and half as many trucks as Dealership A. So, the equation for the total cars and trucks for Dealership B can be written as:
2C + (1/2)T = 300

c) From the equation in part a), we can say that Dealership A sold a total of C cars.

d) Given that Dealership B sold half as many trucks as Dealership A, we can substitute the value of T from part a) into the equation in part b) to find the number of trucks sold by Dealership B:
2C + (1/2)(T from part a)) = 300
2C + (1/2)(225 - C) = 300
2C + (112.5 - 0.5C) = 300
2C - 0.5C = 300 - 112.5
1.5C = 187.5
C = 187.5 / 1.5
C = 125

Therefore, Dealership A sold 125 cars (Answer to part c) and we can substitute this value back into the equation in part a) to find the number of trucks sold by Dealership A:
125 + T = 225
T = 225 - 125
T = 100

Dealership B sold 125 cars and 100 trucks (Answer to part d).

Answer 4

Joelle currently has 18 rocks in her collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week. Set up a system of equations to show how many rocks each has in their collection.(6 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. a) Joelle has y = Response areax + Response area b) Lewis has y = Response areax + Response area c) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? Response area weeks d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.

Answer 5

[AI-generated answer — Bot GPT 3.5]

a) Joelle has y = 18 + 4x

b) Lewis has y = 30 + 3x
c) To find the number of weeks when Joelle and Lewis have the same number of rocks, we can set the two equations equal to each other and solve for x:
18 + 4x = 30 + 3x
x = 12
So, after 12 weeks, Joelle and Lewis will have the same number of rocks in their collections.
d) To find the number of rocks Joelle and Lewis will have when the amount of rocks in their collections is equal, we substitute x = 12 into either equation:
Joelle: y = 18 + 4(12) = 18 + 48 = 66 rocks
Lewis: y = 30 + 3(12) = 30 + 36 = 66 rocks
So, they will both have 66 rocks in their collection.

Answer 6

Joyce wants to go to the zoo with her friend over spring break. You can pay $45 to get into the zoo each time, or join a membership for $50 and then only pay $20 each visit to the zoo. How many times will Joyce need to visit the zoo to justify the expense of the membership fee?

Answer 7

[AI-generated answer — Bot GPT 3.5]

To determine how many times Joyce will need to visit the zoo to justify the expense of the membership fee, we need to compare the total cost of paying for individual visits with the cost of joining the membership.

Let's assume Joyce needs to visit the zoo "x" times.

If Joyce pays $45 for each visit, the total cost of individual visits would be 45x.

If Joyce decides to join the membership for $50, she would need to pay an additional $20 for each visit. So, the total cost with the membership would be 50 + 20x.

To justify the expense of the membership fee, the total cost of individual visits should be equal to or greater than the cost with the membership. Therefore, we can set up the equation:

45x ≥ 50 + 20x

Now, let's solve the equation to determine the minimum number of visits Joyce needs to justify the expense of the membership fee:

45x - 20x ≥ 50
25x ≥ 50
x ≥ 2

So, Joyce will need to visit the zoo at least 2 times to justify the expense of the membership fee.

Answer 8

Put the steps in order that are used to solve the following systems of equations by substitution. −7x−2y=−13 x−2y=11

Answer 9

[AI-generated answer — Bot GPT 3.5]

1) Solve one of the equations for one variable in terms of the other variable.

2) Substitute the expression from step 1 into the other equation.
3) Solve the resulting equation for a single variable.
4) Substitute the value found in step 3 back into one of the original equations to find the value of the other variable.
5) Write the solution as an ordered pair (x, y), where x and y are the values found in steps 3 and 4.