Question

At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?

Answer 1

The cost of a chicken shawarma wrap is $10.99 and the cost of one order of spiced potatoes is $4.99.

Explanation:

X denotes the cost of a chicken shawarma wrap and Y denotes the cost of an order of spiced potatoes.

From the provided information we can form two equations for the total price paid by Ms. Ironperson and Mr. Thoro.

`3x+2y=42.95...(i)\\5x+4y=74.91...(ii)`

Multiply (i) by 4 and (ii) by 2 and subtract the two resulting equations:

`3x+2y=42.95\ \ \ ]* 4\\5x+4y=74.91\ \ \ ]*2\\\\\Rightarrow\\\\12x+8y=171.80\\10x+8y=149.82\\\\\text{subtract}\\\\2x=21.98\\\\x=10.99`

Substitute x = 10.99 in (i) and solve for y as follows:

`3x+2y=42.95\\\\(3* 10.99)+2y=42.95\\\\2y=9.98\\\\y=4.99`

Thus, the cost of a chicken shawarma wrap is $10.99 and the cost of one order of spiced potatoes is $4.99.