Eric, Peyton and Nathan go to a Chinese restaurant from lunch and order three different platters. Eric orders 2 portions of fried rice and 1 portion of chow mien. Peyton ordered 1 portion of fried rice, 1 portion of chow mien and 1 portion of sauteed broccoli. Nathan ordered 1 potion of sauteed broccoli and 2 portions of chow mien. Eric paid $5, Peyton paid $5.25 and Nathan paid $5.75 for their meals. How much does each item cost? *

Step-by-step explanation:

Step 1: Create expressions

Assume that fried rice is x

Assume that chow mein is y

Assume that sauteed broccoli is z

Expression for Eric's order would be;

x + y = 5

Expression for Peyton's order would be;

x + y + z = 5.25

Expression for Nathan's order would be;

2y + z = 5.75

Step 2: Express in like terms

Now express z and x in terms of y so that we can solve for y;

2y + z = 5.75                                                           x + y = 5

z = 5.75 - 2y                                                            x = 5 - y

Step 3: Solve variables

Solve for y

x + y + z = 5.25

(5 - y) + y + (5.75 -2y) = 5.25

5 + 5.75 - 2y = 5.25

10.75 - 2y = 5.25

2y = 10.75 - 5.25

2y = 5.5

y = $2.75

Solve for x;

x = 5 - y

= 5 - 2.75

= $2.25

Solve for z;

= 5.75 - 2y

= 5.75 - 2 * 2.25

= $0.25

Fried rice is $2.25

Chow mien is $2.75

Sauteed broccoli is $0.25

the first for the first one and the second for the second