South Wind Vineyards uses 820 acres to plant Chardonnay and Riesling grapes. The vintner knows the profits will be greatest by planting 140 more acres of Chardonnay than Riesling. How many acres of each type of grape should be planted?


Answered 1 year ago
Answered 1 year ago
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We will use the elimination method to solve the equations. let cc be the total acres of Chardonnay grapes and rr be the total acres of Riesling grapes. Since their sum is 820820 and their Chardonnay is 140140 acres more than Riesling, then:

c+r=820cr=140\begin{aligned} c+r&=820\\ c-r&=140 \end{aligned}

We will eliminate one variable (c)(c), solve for rr and then use the value of rr to solve for cc

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