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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.

Respuesta :

MrRoyal

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:

[tex]2T + C + M = 14.74[/tex] --- (1)

For Mia:

[tex]5T + 2C + M = 29.05[/tex] -- (2)

[tex]M = 3C[/tex]

Required

Determine the cost of each item

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

[tex]2T + C + M = 14.74[/tex]

[tex]2T + C + 3C = 14.74[/tex]

[tex]2T + 4C = 14.74[/tex] --- (4)

[tex]5T + 2C + M = 29.05[/tex]

[tex]5T + 2C + 3C = 29.05[/tex]

[tex]5T + 5C = 29.05[/tex] --- (5)

Divide through (5) by 5

[tex]T + C = 5.81[/tex]

Solve for C

[tex]C= 5.81 - T[/tex]

Substitute 5.81 - T for C in (4)

[tex]2T + 4C = 14.74[/tex]

[tex]2T + 4(5.81 - T) = 14.74[/tex]

[tex]2T + 23.24 - 4T = 14.74[/tex]

Collect Like Terms

[tex]2T - 4T = 14.74 - 23.24[/tex]

[tex]-2T= -8.5[/tex]

Solve for T

[tex]T = -8.5/-2[/tex]

[tex]T = 4.25[/tex]

Recall that:

[tex]C= 5.81 - T[/tex]

[tex]C = 5.81 - 4.25[/tex]

[tex]C = 1.56[/tex]

Recall that

[tex]M = 3C[/tex]

[tex]M = 3 * 1.56[/tex]

[tex]M = 4.68[/tex]

Hence:

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

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