If the prime rib is three times as expensive as a side dish, what is the cost of each item?

Question

At Marty’s Fine Cuisine, meals are served a la carte. That is, each item on

the menu is priced separately. Marina and Taylor went to Marty’s to

celebrate their getting an A on the Algebra I test. Marina ordered prime

rib, 2 side dishes, and a roll. Taylor ordered prime rib, 3 side dishes, and 2

rolls. Marina’s meal came to $36 and Taylor’s meal came to $44. If the

prime rib is three times as expensive as a side dish, what is the cost of each

item?

Do this using some type of systems of linear equations.

Answer 1

P=3S

P+3S+2R=44

P+2S+R = 36

Multiply 2nd equation by 2 and subtract the 1st equation from that doubled equation

2P + 4S + 2R =72

P + 3S + 2R = 44

P+S = 72-44 = 28

P=3S, substitute

to get 3S + S = 28

4S = 28

S = 28/4 = 7

P= 3S = 3(7) = 21

P+2S + R = 36

21+ 2(7) + R = 36

21+14 + R =36

R = 36-35 = 1

Roll costs $1, Prime rib $21 Sides $7