Question

please hlelp meYou found a Chinese restaurant and ordered three different luncheon combination platters. Mom ordered 2 portions of fried rice and 1 portion of chicken chow mein. Your sister ordered 1 portion of fried rice, 1 portion of chicken chow mein, and 1 eggroll. You ordered 2 portions of chicken chow mein and 1 eggroll. Your mother’s platter cost $5, your sister’s cost $5.25, and yours cost $5.75. How much did 1 eggroll cost?

Answer 1

Let's use the variable x to represent the cost of the rice, y to represent the cost of the chicken and z to represent the cost of the eggroll.

2 rices and 1 chicken cost $5, so:

$2x+y=5$

1 rice, 1 chicken and 1 egg cost $5.25, so:

$x+y+z=5.25$

2 chickens and 1 egg cost $5.75, so:

$2y+z=5.75$

From the first equation, we have y = 5 - 2x. Using this value on the other two equations, we have:

$\begin{gathered} x+(5-2x)+z=5.25\\ \\ -x+z=0.25\\ \\ \\ \\ 2(5-2x)+z=5.75\\ \\ -4x+z=-4.25 \end{gathered}$

From the new second equation, we have x = z - 0.25. Using this value in the new third equation, we have:

$\begin{gathered} -4(z-0.25)+z=-4.25\\ \\ -4z+1+z=-4.25\\ \\ -3z=-5.25\\ \\ z=1.75 \end{gathered}$

Therefore the cost of 1 eggroll is $1.75.