The cost of each type of truck is:
$60,000 for the large truck and $45,000 for the small truck
Step-by-step explanation:
A business with two locations buys seven large delivery trucks and
five small delivery trucks the given is:
1. Location A receives three large trucks and two small trucks for a
total cost of $270,000
2. Location B receives four large trucks and three small trucks for a
total cost of $375,000
Assume that the cost of the large truck is $x, and the cost of the small
truck is $y
∵ Location A receives 3 large trucks and 2 small trucks for a total
cost of $270,000
∴ 3x + 2y = 270,000 ⇒ (1)
∵ Location B receives 4 large trucks and 3 small trucks for a total
cost of $375,000
∴ 4x + 3y = 375,000 ⇒ (2)
Let us solve the system of equations to find x and y
Multiply equation (1) by -3 and equation (2) by 2 to eliminate y
∵ (-3)(3x) + (-3)(2y) = (-3)(270,000)
∴ -9x - 6y = -810,000 ⇒ (3)
∵ (2)(4x) + (2)(3y) = (2)(375,000)
∴ 8x + 6y = 750,000 ⇒ (4)
Add equations (3) and (4)
∴ -x = -60,000
- Divide both sides by -1
∴ x = 60,000
∴ The cost of the large truck is $60,000
Substitute the value of x in equation (1) to find y
∵ 3(60,000) + 2y = 270,000
∴ 180,000 + 2y = 270,000
- Subtract 180,000 from both sides
∴ 2y = 90,000
- Divide both sides by 2
∴ y = 45,000
∴ The cost of the small truck is $45,000
The cost of each type of truck is:
$60,000 for the large truck and $45,000 for the small truck
Learn more:
You can learn more about equations in brainly.com/question/3739260
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