Question

A chef is making 20 pounds of fruit salad to sell in his shop. The chef will use only grapes and

blueberries in the fruit salad. Let x and y be defined as follows:

x = the number of pounds of grapes the chef will use

· y = the number of pounds of blueberries the chef will use

a. Write an equation in terms of x and y that can be used to represent the total number of pounds

of fruit salad the chef will make.

Grapes cost $2.50 per pound, and blueberries cost $4.00 per pound. The chef spent a total of $59.00

for grapes and blueberries for the fruit salad.

b. Write an equation in terms of x and y that can be used to represent the total cost, in dollars, of

the fruit salad.

c. Use your answers from parts (a) and (b) to determine the number of pounds of grapes and the

number of pounds of blueberries the chef will use to make the fruit salad. Show or explain how

you got your answer.

Answer 1

a) x + y = 20

b) 2.50(x) + 4.00(y) = 59.00

c) Number of pounds of grapes is 14 and that of blueberries is 6

Explanation:

First question says to write an equation in terms of x and y that can be used to represent the total number of pounds

----- Sincex represent the number of pounds of grapes and y represent the number of pounds of blueberries

X + y = 20

The second question says to write an equation in terms of x and y that can be used to represent the total cost, in dollars, of the fruit salad.

----- since x = total number of pounds of grapes bought and y is same for blueberries and both at prices of $2.50 and $4.00 respectively and at a total cost of $59

2.5x + 4y = 59

Third question says to Use your answers from parts (a) and (b) to determine the number of pounds of grapes and the number of pounds of blueberries the chef will use to make the fruit salad

-----X + y = 20___ equation 1

2.5x + 4y = 59_____ equation 2

Now multiply equation 1 by 5

And equation 2 by 2 so as to have the coefficient of y in both equation to be same.

5x + 5y = 100____ equation 3

5x + 8y = 118_____ equation 4

Subtract equation 3 from 4 and we have:

3y = 18

Y = 6

Replace y = 6 in equation 4

5x + 8y = 118

5x + (8 × 6) = 118

5x + 48 = 118

5x = 70

X = 70/5

X = 14