Help me! I'll fan, give medals, I just need help!

A dealer has a lot that can hold 30 vehicles. In this lot, there are two available models, A and B. The dealer normally sells at least twice as many model A cars as model B cars. If the dealer makes a profit of $1300 on model A cars and $1700 on model B cars, how many of each car should the dealer have in the lot given that the total profit for the sale of both cars is $43,000?

a. 20 model A
10 model B

b. 10 model A
20 model B

c. 5 model A
25 model B

d. 16 model A
14 model B

i would appreciate if you explained!

Question

Help me! I'll fan, give medals, I just need help!

A dealer has a lot that can hold 30 vehicles.  In this lot, there are two available models, A and B.  The dealer normally sells at least twice as many model A cars as model B cars.  If the dealer makes a profit of $1300 on model A cars and $1700 on model B cars, how many of each car should the dealer have in the lot given that the total profit for the sale of both cars is $43,000?

a. 20 model A
10 model B

b. 10 model A
20 model B

c. 5 model A
25 model B

d. 16 model A
14 model B


i would appreciate if you explained!

anonymous · Answer

Which can we rule out ?

anonymous · Answer

I really have no idea, I'm just stumped

whpalmer4 · Answer

two models, A and B.  Let A be the number of model A cars, and B the number of model B cars.

A+B=30

Total profit is $43,000, and comes from $1300 for each model A and $1700 for each model B:

1300*A + 1700*B = 43000

Do you know how to solve such a system of equations?

anonymous · Answer

No, i have no idea

whpalmer4 · Answer

Okay.  The first equation can easily by solved to give you one variable in terms of the other.  Do that, then substitute the expression for the one variable in place of the other in the second equation.

Which letter do you like better, A or B?

anonymous · Answer

A

whpalmer4 · Answer

Okay, solve the equation $$A + B = 30$$ for $A$.  What do you get?

anonymous · Answer

yes it is A you are correct :)

whpalmer4 · Answer

No, I wasn't asking about answer, I'm trying to teach @yazmined how to actually solve the problem.

anonymous · Answer

If you solve for a you'd get 30 right?

whpalmer4 · Answer

$$A+B=30$$subtract B from both sides to give us A alone on one side and everything else on the other
$$A+B-B = 30 - B$$$$A = 30-B$$
That's not an actual value yet, but it will help us get to one.

Now we take the second equation:
$$1300A + 1700B = 43000$$Everywhere we see $A$, we replace it with $(30-B)$

What do you get if you do that?

anonymous · Answer

1300(30-B) +1700B = 4300

whpalmer4 · Answer

oops, that should be$$1300(30-B)+1700B = 43000$$ (you left off a 0)

Now, can you distribute the left side of that?  What do you get?

whpalmer4 · Answer

@yazmined Do you see how to finish, or have you given up?