Question

One day me. Anderson brought to the farmers market the greatest number of pounds of fruit that he can carry in his truck, He brought two kinds of fruit : apples and peaches. He sells the apples for $2.50 per pound and sells the peaches for $3.25 per pound. That day, Mr.Anderson sold all the fruit he brought to the farmers market for a total of $2,497. How many pounds of apples and how many pounds of peaches did he sell that day?

Answer 1

998.8 pounds

Explanation:

Let a be the number of apple pound and p is the number of peach pound.

We want to maximize the total of a and b.

From the total amount he earned from the farmer market at the end of the day we can have the following equation:

2.5a + 3.25p = 2497 or

`a=(2497-3.25p)/(2.5)=998.8-1.3p`

So the total number of pound of fruits that he carries in his truck is

`Total = a + p = 998.8 - 1.3p + p = 998.8 - 0.3p`

Since p is a real mass so p must ≥ 0. That means:

`-0.3p \leq 0`

`998.8 - 0.3p \leq 998.8`

`Total \leq 998.8`

So the greatest number of pounds Anderson can carry in his truck is 998.8 pounds, all apples.