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

Answer:

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

Step-by-step 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