A business with two locations buys seven large delivery vans and five small delivery vans. Location A
receives 5 large vans and 2 small vans for a total cost
of $235,000. Location B receives 2 large vans and 3
small vans for a total cost of $160,000. What is the
cost of each type of van? Use x for the price of a large
van and y for the price of a small van.

The price of a large van, x and price of a small van, y is $35,000 and $30,000 respectively

Given:

large van = x

small van = y

Location A

5x + 2y = 235,000

Location B:

2x + 3y = 160,000

5x + 2y = 235,000 (1)

5x + 2y = 235,000 (1)2x + 3y = 160,000 (2)

multiply (1) by 3 and (2) by 2

15x + 6y = 705,000 (3)

4x + 6y = 320,000 (4)

subtract (4) from (3)

15x - 4x = 705,000 - 320,000

11x = 385,000

x = 385,000 / 11

x = 35,000

substitute x into (2)

2x + 3y = 160,000

2(35,000) + 3y = 160,000

70,000 + 3y = 160,000

3y = 160,000 - 70,000

3y = 90,000

y = 90,000 / 3

y = 30,000

Therefore, the price of a large van, x and price of a small van, y is $35,000 and $30,000 respectively.

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price of a large van = $35000

price of a small van = $30000

Explanation:

Let the price of a large van = x

Let the price of a small van = y

Since A receives 5 large vans and 2 small vans for a total cost of $235,000. Location B receives 2 large vans and 3

small vans for a total cost of $160,000. This can be written as:

5x + 2y = 235000 i

2x + 3y = 160000 ii

Multiply equation i by 2

Multiply equation ii by 5

10x + 4y = 470000 iii

10x + 15y = 800000 iv

Subtract iii from iv

11y = 330,000

y = 330000/11.

y = 30,000

From equation I,

5x + 2y = 235000

5x + 2(30000) = 235000

5x + 60000 = 235000

5x = 235000 - 60000

5x = 175000

x = 175000 / 5

x = 35000

Therefore, price of a large van = 35000

price of a small van = 30000

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