SOLUTION: A company with two stores buys six large delivery vans and five small delivery vans. The first store receives four large vans and 2 small vans for a coast of $160,000. The second

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Question 1188417: A company with two stores buys six large delivery vans and five small delivery vans. The first store receives four large vans and 2 small vans for a coast of $160,000. The second store receives two large delivery vans and three small delivery vans for a cost of $128,000. Find the cost for each type of delivery van.
Found 2 solutions by Shin123, MathTherapy:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the cost of the large van, and y be the cost of the small van. We have the system of equations system%284x%2B2y=160000%2C2x%2B3y=128000%29.
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 2*y to the right, we get:
4%2Ax+=+160000+-+2%2Ay, or x+=+160000%2F4+-+2%2Ay%2F4. Substitute that
into another equation:
2%2A%28160000%2F4+-+2%2Ay%2F4%29+%2B+3%5Cy+=+128000 and simplify: So, we know that y=24000. Since x+=+160000%2F4+-+2%2Ay%2F4, x=28000.

Answer: system%28+x=28000%2C+y=24000+%29.

Therefore, the cost of the large van is $28,000 and the cost of the small van $24,000.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A company with two stores buys six large delivery vans and five small delivery vans. The first store receives four large vans and 2 small vans for a coast of $160,000. The second store receives two large delivery vans and three small delivery vans for a cost of $128,000. Find the cost for each type of delivery van. 
In MANY cases, this solver that the other person used, is one of, if not the worst method that anyone could use to solve this problem.

I can't see how the person who responded couldn't see that when it's all so clear.

Let the cost of one large and one small van be L and S, respectively

Then we get: 4L + 2S = 160,000____2(2L + S) = 2(80,000)____2L + S = 80,000 ------ eq (i)

Also, 2L + 3S = 128,000 ------ eq (i)

2S = 48,000 ----- Subtracting eq (i) from eq (ii)

Cost of each small van, or 

Now you can find the cost of each large van.