Question

At Sam's a soda and 2 slices of everything pizza cost $10.25. At Two Cousins' a soda and 4 slice of everything pizza cost $18.75. The costs are the same at both places. What is the cost of 1 slice of pizza and 1 soda?

Answer 1

Explanation:

1 soda 2 pizza = cost 1 soda 4 pizza = cost

1x+2y=10.25 1x+4y=18.75

Rewrite equations:

x+2y=10.25;x+4y=18.75

Step: Solvex+2y=10.25for x:

x+2y=10.25

x+2y+−2y=10.25+−2y(Add -2y to both sides)

x=−2y+10.25

Step: Substitute−2y+10.25forxinx+4y=18.75:

x+4y=18.75

−2y+10.25+4y=18.75

2y+10.25=18.75(Simplify both sides of the equation)

2y+10.25+−10.25=18.75+−10.25(Add -10.25 to both sides)

2y=8.5

2y

2=8.5

STEP 2(Divide both sides by 2)y=4.25

Step: Substitute4.25foryinx=−2y+10.25:

x=−2y+10.25

x=(−2)(4.25)+10.25

x=1.75(Simplify both sides of the equation)

Answer:

x=1.75 and y=4.25