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.

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:

--- (1)

For Mia:

-- (2)

Required

Determine the cost of each item

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

--- (4)

--- (5)

Divide through (5) by 5

Solve for C

Substitute 5.81 - T for C in (4)

Collect Like Terms

Solve for T

Recall that:

Recall that

Hence:

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

1) Statement: Angle 2 and angle 5 are supplementary

Reason: Given

2) Statement : Angle 2 and angle 3 are congruent.

Reason: Vertically Opposite Angles are always congruent.

3) Statement: If angle 2 is congruent to angle 3 and and angle 2 is supplementary to angle 5, then angle 3 is supplementary to angle 5.

Reason: Substitution Property

4) Statement: Line l is parallel to line m.

Reason: Converse of the the Same-Side Interior Angles Theorem (If two lines are cut by a transversal and the consecutive interior angles are supplementary, then the lines are parallel.)