math help question

Question

this year the state highway department in Montana purchased

192

identical cars and

172

identical trucks for official use. The purchase price was

​$5,338,256.

Due to a budget​ shortfall, next year the department plans to purchase only

64

cars and

101

trucks. It will be charged the same price for each car and each truck. Next​ year, it plans to spend

​$2,561,052.

How much does the department pay for each car and for each​ truck?

Answer 1

You want to arrange your question in a system of equations. We'll use "C" for cars and "T" for trucks:

192C + 172T = $5,338,256

64C + 101T = $2,561,052

Now you need to eliminate one of the variables. Fortunately, in this case, 64 happens to be a multiple of 192 (64 x 3 = 192). So you want to take the bottom equation and multiple by -3 so you can eliminate the C's. You should get:

-192C - 303T = -$7,683,156

Now take your first equation and combine it for a new system of equations:

192C + 172T = $5,338,256

-192C - 303T = - $7,683,156

--------------------------------------

The C's are eliminated leaving: -131T = -2,344,900. Divide both sides by -131 and you'll get

T = $17,900. Each truck cost $17,900.

Go back to either equation - I'll use the second since it's smaller: 64C + 101T = $2,561,052. Plug in $17,900 for T and you get:

64C + 101($17,900) = $2,561,052 or

64C + $1,807,900 = $2,561,052 - then subtract $1,807,900 from both sides

64C = $753,152

C or each car equals: $753,152 / 64. (I'll let you find the final answer yourself).

To check your answer, plug in both C and T into either equation. You'll find you'll get a matching answer. Hope this helps. Feel free and reach out if you have questions!