Question

Grace, Jessica and Mia went out to dinner after the Volleyball game. Jessica bought two tacos, a coke and a mango smoothie and spent $14.74. Grace bought Mia's dinner. She bought 5 tacos, 2 cokes and 1 mango smoothie and spent $29.05. The mango smoothie cost three times as much as the coke. Determine the price of each item. Answer in a complete sentence.

Answer 1

A mango costs $4.68, a coke costs $1.56 and a taco costs $4.25

Explanation:

Given

Represent Tacos with T, Coke with C and Mango with M

For Grace:

`2T + C + M = 14.74` --- (1)

For Mia:

`5T + 2C + M = 29.05` -- (2)

`M = 3C`

Required

Determine the cost of each item

Substitute 3C for M in (1) & (2)

`2T + C + M = 14.74`

`2T + C + 3C = 14.74`

`2T + 4C = 14.74` --- (4)

`5T + 2C + M = 29.05`

`5T + 2C + 3C = 29.05`

`5T + 5C = 29.05` --- (5)

Divide through (5) by 5

`T + C = 5.81`

Solve for C

`C= 5.81 - T`

Substitute 5.81 - T for C in (4)

`2T + 4C = 14.74`

`2T + 4(5.81 - T) = 14.74`

`2T + 23.24 - 4T = 14.74`

Collect Like Terms

`2T - 4T = 14.74 - 23.24`

`-2T= -8.5`

Solve for T

`T = -8.5/-2`

`T = 4.25`

Recall that:

`C= 5.81 - T`

`C = 5.81 - 4.25`

`C = 1.56`

Recall that

`M = 3C`

`M = 3 * 1.56`

`M = 4.68`

Hence:

A mango costs $4.68, a coke costs $1.56 and a taco costs $4.25