Answer:
Cost of the one fruit bowl is $3 .
Step-by-step explanation:
Let us assume that the cost of salad be x .
Let us assume that the cost of fruit bowl is y .
Let us assume that the cost of the sandwiches is z .
As given
At Snack Palace, the Bishop family pays $12 for a salad, fruit bowl, and two sandwiches.
Equation becomes
x + y + 2z = 12
The Cortez family pays $14 for two salads and two sandwiches.
Equation becomes
2x + 2z = 14
Simplify the above
x + z = 7
The Donovan family pays $14 for a salad and three fruit bowls.
Equation becomes
x + 3y = 14
Thus three equations are
x + y + 2z = 12
x + z = 7
x + 3y = 14
Multiply x + z = 7 by 2 and subtracted from x + y + 2z = 12.
x -2x + y + 2z -2z = 12 - 14
-x + y = -2
Add the equations -x + y = -2 and x + 3y = 14 .
Add both the above equations
x -x + 3y + y = 14 -2
4y = 12
[tex]y = \frac{12}{4}[/tex]
y = $3
Therefore the cost of the one fruit bowl is $3 .
