Answer:
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.
