Question

POSSIBLE POINTS: 3.33

Tracy wants to buy some pies for her sisters and she has a budget of $82 to spend on $5

apple pies, $4.5 banana pies, and $5.5 chocolate pies. She wants to buy 16 pies for her

sisters and must buy as many chocolate pies as apple pies and banana pies combined.

How many of each item should she buy? Write a system of equations to help you solve

this problem.

# of applie pies =

# of banana pies =

# of chocolate piles =

1

2 3

Answer 1

From the information given, you can write the following system of equations:

x+y+z=16 (1)

5x+4.5y+5.5z=82 (2)

z=x+y (3)

You can replace (3) in (1) and (2):

x+y+x+y=16

2x+2y=16 (4)

5x+4.5y+5.5(x+y)=82

5x+4.5y+5.5x+5.5y=82

10.5x+10y=82 (5)

Now, you have the following equations:

2x+2y=16 (4)

10.5x+10y=82 (5)

You can isolate x in (4):

2x=16-2y

x=8-y (6)

Then, you have to replace (6) in (5):

10.5(8-y)+10y=82

84-10.5y+10y=82

84-82=10.5y-10y

2=0.5y

y=2/0.5

y=4

Now, you can replace the value of y in (6) to find x:

x=8-4

x=4

Finally, you can replace the vaue of x and y in (3) to find z:

z=4+4

z=8

According to this, she should buy 4 apple pies, 4 banana pies and 8 chocolate pies.