Algebraic system of equations

Question

Two friends went to a restaurant and ordered one plain pizza and two sodas. Their bill totaled $20.52. Later that day, five friends went to the same restaurant. They ordered 3 plain pizzas and each person had one soda. Their bill totaled $50.94. Solve a system of equations to determine the price of one plain pizza.

Answer 1

P+2S = 20.52 multiply by 3 to get

3P+6S = 61.56 subtract the 2nd equation

3P+5S = 50.94

S=$10.62 for a soda

plug that into the 1st equation to solve for the price of a pizza

P+2(10.62) = 20.52

P= 20.52 - 21.24= -72 cents. They're giving away not only free pizza but paying the customer 72 cents to take the pizza

You may have a typo in the problem somewhere

prices don't make sense

UNLESS, the "5" friends each shared just 1 soda, along with 3 pizzas

then the numbers make sense

that gives 2 equations:

3P+S = 50.94

P+2S=20.32, multiply 1st equation by 2 and subtract the 2nd equation

6P+2S = 101.88

P+2S = 20.32

5P = 81.36

P= $16.27 for a pizza

S= $2.13 for a soda