two friends went to a restaurant and ordered one plain pizza and two sodas. their bill totaled $15.95. later that day, five frie nds 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?
1 answer:
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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