How do I solve this word problem ?

Question

Fred, George, and Juan went to eat Mexican food. They all ordered from a combination plate. Fred ordered 3 tacos, 1 enchilada, and 2 tamales; his bill was $14.50 before tax. George ordered 2 tacos, 2 enchiladas, and 2 tamales; his bill ws $13 beofre tax. Juan ordered 1 taco, 4 enchiladas, and 1 tamale; his bill was $11 before tax. How much was each taco? each enchiliada, and each tamale?

Answer 1

Let x represent cost of one taco, y represent cost of one enchilada, z represent cost of one tamale

Fred (3 tacos, 1 enchilada, 2 tamales) spends $14.50

3x + 1y + 2z = 14.50

George:

2x + 2y + 2z = 13

Juan:

1x + 4y + 1z = 11

This is a system of 3 linear equations with 3 unknowns. There are several ways to solve such a system--you are likely using addition/elimination. The idea is to pick a variable and eliminate it from two different pairs of equations.

Let's eliminate z.

A) 3x + y + 2z = 14.5

B) 2x + 2y + 2z = 13

C) x + 4y + z = 11

Eliminate z from A and C by multiplying C by -2 and adding to A.

A) 3x + y + 2z = 14.5

C') -2x -8y -2z = -22

A) + C): x - 7y = -7.5

Eliminate z from B) and C) by multiplying C by -2 and adding to B.

B) 2x + 2y +2z = 13

C')-2x -8y -2z = -22

B)+C): -6y = -9 (this usually does not happen by x was eliminated too)

y = 3/2 or $1.50

Use equation for A + C to determine x (now that we know y):

x - 7(3/2) = -15/2

x = -15/2 + 21/2

x = 6/2 = $3

Use equation C to determine z:

3 + 4(7/2) + z = 11

9 + z = 11

z = $2

Cost of a Taco: $3

Cost of an Enchilada: $1.50

Cost of a Tamale: $2

You can check these results by determining how much was spent by each of Fred, George, and Juan. Left to you.