Problema Solution

2. 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.

a. Use x to represent Chardonnay grapes and y to represent Riesling grapes. Write an equation that illustrates the total number of acres between the two grapes.

b. Write an equation that illustrates how many more acres of Chardonnay there are than Riesling.

c. Use the equations from Parts a. and b. of this exercise as a system of equations. Use substitution or elimination to determine how many of each type of grape should be planted. Describe the steps you used to solve the problem.

Answer provided by our tutors

a. x + y = 820

 

b. x = y + 140

 

c. y + 140 + y = 820

2y + 140 = 820

2y = 680

y = 340

 

x = 140 + y

x = 140 + 340

x = 480

 

so there are 480 acres of chardonnay and 340 acres of riesling