A farmer has a field that is 110
3 over 4
3
4
acres. She wants to separate it into 5 equally-sized sections. In one section, she plants a crop that will cost her $67.25 per acre. How much will it cost her to plant the crop in this section?
The field is 110
3 over 4
3
4
, it will be separated into 5 sections, and the cost per acre is $67.25.
What are you given?
What does the problem ask for?
The problem asks for the cost to plant one section.
Step 2: Make a plan.
What is your plan to solve this problem?
Either one of Nathan’s plans will work.
Plan 1:
Convert 110
3 over 4
3
4
to the decimal, 110.75. Divide 110.75 by 5 sections to determine the size of each section. Multiply the quotient by $67.25 to determine the cost to plant in one section of the field.
Plan 2:
Divide 110
3 over 4
3
4
by 5 to determine the size of each section. Write $67.25 as the fraction $67
1 over 4
1
4
, and then multiply by the quotient to determine the cost to plant in one section of the field.
Do either one of the plans need to worry about the order of operations?
Yes, but parenthesis are not necessary since the problem only uses division and multiplication.
Step 1: Understand the problem.
Write an equation that models each one of Nathan’s plans that you could use to solve for final cost, C.
Plan 1:
C = 110.75 ÷ 5 × $67.25
Plan 2:
C = 110
3 over 4
3
4
÷ 5 × $67
3 over 4
3
4
Step 3: Do the plan.
What is the cost to plant the crop? Round to the nearest cent if necessary.
C = $1,489.59. The cost to plant the crop in one section is $1,489.59.
Step 4: Check your answer for reasonableness.
Strategy check: Use rounding to estimate your answer.
Round
110
3 over 4
3
4
to the nearest hundred and $67.25 to the nearest ten.
110
3 over 4
3
4
≈ 100;
$67.25 ≈ $70
Divide 100 by 5 to estimate the size of one section, and then multiply by the approximate cost of planting one acre of the crop.
100 ÷ 5 = 20
20 × $70 = $1,400
Compare your estimate to your actual answer.
The estimate of $1,400 is close to the actual answer of $1,489.59, so our answer is reasonable.
