Question

A trucker buys crates of apples and pears to sell at a Farmer's Market. The apples cost $6 per crate and the pears cost $5.50 per crate. Each crate weights 25 pounds. If the truck can carry 5000 pounds and the trucker has $1180 to spend, how many crates of each kind of fruit can he buy? Write your answer as an ordered pair (x,y).

Answer 1

He can buy 160 crates of apples and 40 crates of pears. (160, 40).

Explanation:

From the information given, you can write the following equations:

25x+25y=5000 (1)

6x+5.50y=1180 (2), where:

x is the number of crates of apples

y is the number of crates of pears

First, you can solve for x in (1):

25x=5000-25y

x=(5000/25)-(25y/25)

x=200-y (3)

Then, you can replace (3) in (2) and solve for y:

6(200-y)+5.50y=1180

1200-6y+5.50y=1180

1200-1180=6y-5.50y

20=0.5y

y=20/0.5

y=40

Finally, you can replace the value of y in (3) to find the value of x:

x=200-y

x=200-40

x=160

According to this, the answer is that he can buy 160 crates of apples and 40 crates of pears. (160, 40).