Answer:
Tracy must buy 4 apple pies, 4 banana pies, and 8 chocolate pies.
Step-by-step explanation:
The complete question would be:
<em>"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 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?
</em>
<em>Write a system of equations of this problem."</em>
Then, we will write a system of equations according to the information given in the problem:
We must consider each type of pie as an unknown, so:
x: the amount of apple pies
y: the amount of banana pies
z: the amount of chocolate pies
As she has a budget of $82, the amount of each pie must be multiplied by its price and the total sum must be 82:
5x + 4.5y + 5.5z =82 (1)
The total amount of pies must be 16:
x + y + z = 16 (2)
And the amount of chocolate pies must be equal to the quantity of apple pies and banana pies combined:
z= x + y (3)
System of equations:
(1) 5x + 4.5y + 5.5z =82
(2) x + y + z = 16
(3) z= x + y
First, we subtract x and y on 3 on both sides:
z - (x + y )= x + y - (x + y)
-x -y +z = 0
Then, we add 2 and 3:
(2) x + y + z = 16
(3) -x -y +z = 0
2 z=16
z=8
We replace the value of z on 3 and substract x on both sides:
x + y =8
y=8 - x
We use this on equation 1:
5x + 4.5y + 5.5z =82
5x + 4.5×(8-x) + 5.5×8=82
5x + 36 - 4.5x + 44 = 82
0.5x + 80 =82
0.5x=82-80
0.5x=2
x=2/0.5
x=4
We replace the values of x and z on equation 2:
x + y + z = 16
4 + y + 8 = 16
y + 12 = 16
y=16-12
y= 4
Tracy must buy 4 apple pies, 4 banana pies, and 8 chocolate pies.
