Question

Heather, Chang, and Justin served a total of 93 orders Monday at the school cafeteria. Chang served 2 times as many orders as Justin. Heather served 5 more orders than Justin. How many orders did they each serve?

Answer 1

Let the # of orders sold by these 3 people be represented by H, C and J.
Then H+C+J=93.
C=2J
H=J+5
Find H, C and J.

Let's eliminate C. Substitute 2J for C in H+C+J=93: H+2J+J = 93
Now let's eliminate H: Subst. J+5 for H in this last equation:

J+5 + 2J + J = 93 => 4J + 5 = 93 => 4J = 88.

Thus, J = 88/4 = 22.

J handles 22 orders.
H handles 22+5 (or 27) orders.
C handles the rest: 2(22) (or 44) orders.

Check: do the numbers 22, 27 and 44 add up to 93, as they must? Yes.

Answer 2

Write an equation where x = Justin's orders
93 = (x) + (2x) + (x + 5)
Simplify the equation:
93 = 4x + 5
Subtract 5 from both sides:
88 = 4x
Divide 4 on both sides:
22 = x
Solve for the orders:
x = 22 = Justin
22(2) = 44 = Chang
22 + 5 = 27 = Heather.


Hope this helps!