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A 300 -acre farm produced 20,000 bushels of corn last year. What is the minimum rate of production, in bushels per acre, that is needed this year so the farm's two-year production total will be at least 49,100 bushels of corn?

A $300$ -acre farm produced $20$ , $000$ bushels of corn last year. What is the minimum rate of production, in bushels per acre, that is needed this year so the farm's two-year production total will be at least $49$ , $100$ bushels of corn?

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GCF and LCM: word problems

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Q. A

300

-acre farm produced

20

,

000

bushels of corn last year. What is the minimum rate of production, in bushels per acre, that is needed this year so the farm's two-year production total will be at least

49

,

100

bushels of corn?

Given Information: Determine the total production needed for two years. $\newline$ The farm needs to produce at least $49,100$ bushels of corn over two years.
Subtract First Year: Subtract the first year's production from the total needed. $\newline$ The farm produced $20,000$ bushels last year, so we subtract this from the two-year total to find out how much more is needed. $\newline$ $49,100$ bushels $-$ $20,000$ bushels $=$ $29,100$ bushels
Calculate Minimum Rate: Calculate the minimum rate of production for the second year. $\newline$ The farm has $300$ acres, and we need to find out how many bushels per acre it needs to produce to meet the two-year goal. $\newline$ Minimum rate of production $= \frac{\text{Needed production for the second year}}{\text{Number of acres}}$ $\newline$ Minimum rate of production $= \frac{29,100 \text{ bushels}}{300 \text{ acres}}$
Final Answer: Perform the division to find the minimum rate of production. $\newline$ Minimum rate of production = $\frac{29,100 \text{ bushels}}{300 \text{ acres}} = 97 \text{ bushels per acre}$

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