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two friends went to a restaurant and ordered one plain pizza and two sodas. their bill totaled $15.95. later that day, five friends went to the alsame restaurant. they ordered three plain pizzas and each person had one soda. their bill totaled $45.90. write and solve a system of equations to determine the price of one plain pizza?

Respuesta :

Americ
x= cost per pizza
y= cost per soda


1ST VISIT TO RESTAURANT
x + 2y= $15.95

2ND VISIT TO RESTAURANT
3x + 5y= $45.90


STEP 1
multiply equation from 1st visit by -3. Will be able to solve by elimination method in step 2.

-3(x + 2y)= -3(15.95)
multiply -3 by each term

(-3 * x) + (-3 * 2y)= (-3 * 15.95)

-3x - 6y= -47.85


STEP 2
add 2nd visit equation to new 1st
visit equation in step 1.

3x + 5y= 45.90
-3x - 6y= -47.85
x term will cancel out; solve for y

-y= -1.95
divide both sides by -1

y= $1.95 per soda


STEP 3
substitute y value in either original equation to solve for x

x + 2y= $15.95

x + (2 * 1.95)= 15.95
multiple in parentheses

x + 3.90= 15.95
subtract 3.90 from both sides

x= $12.05 per pizza


CHECK
3x + 5y= $45.90
3(12.05) + 5(1.95)= 45.90
36.15 + 9.75= 45.90
45.90= 45.90


ANSWER: Each pizza costs $12.05 and each soda costs $1.95.

Hope this helps! :)

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