Question

Peter hired two combine operators to harvest his 260 acres of wheat. He expected a yield of 50 bushels per acre. The first operator had a 3% grain loss, and the second operator had 5% grain loss. Each operator harvested the same number of acres in the same time. How much was saved by the first operator if wheat sold for $11.97 perbushel?

Answer 1

The amount in dollars of wheat saved by the first operator is;

`\text{ \$1,556.10}`

Step-by-step explanation:

Given that Peter hired two combine operators to harvest his 260 acres of wheat.

And it yeilds 50 bushels per acre.

The total amount of bushels of wheat on the field is;

`\begin{gathered} T=260*50 \\ T=13,000\text{ bushels} \end{gathered}`

Since each operator harvest the same amount;

`\text{opertor 1= Operator 2 = }(13000)/(2)=6500\text{ bushels each}`

If operator 1 loss 3%, the remaining amount is;

`\begin{gathered} A_1=6500-3\text{ \% of 6500} \\ A_1=6500-(0.03)6500 \\ A_1=6305\text{ bushels} \end{gathered}`

Operator 2 loss 5%, the remaining amount is;

`\begin{gathered} A_2=6500-0.05(6500) \\ A_2=6175\text{ bushels} \end{gathered}`

The amount of bushels save by the first operator compared to the second operator is;

`\Delta A=A_1-A_2=6305-6175=130\text{ bushels}`

if wheat is sold for $11.97 per bushel, the amount in dollars of wheat saved by the first operator is;

`\begin{gathered} C=130\text{ bushels }*\text{ \$11.97 per bushel} \\ C=\text{ \$1,556.10} \end{gathered}`

The amount in dollars of wheat saved by the first operator is;

`\text{ \$1,556.10}`