Question

two customers went to eat at burger barn and ordered some burgers and fries. each burger costs the same amount and each order of fries cost the same amount

• the first customer paid $20.70 for 4 burgers and 3 orders of fries.
• the second customer paid $29.00 for 5 burgers and 5 orders of fries.

what is the cost for one order of fries?

Explanation:

Step1: Define Variables

Let \( b \) be the cost of one burger (in dollars) and \( f \) be the cost of one order of fries (in dollars).

Step2: Set Up Equations

From the first customer: \( 4b + 3f = 20.70 \) (Equation 1)
From the second customer: \( 5b + 5f = 29.00 \). We can simplify this by dividing both sides by 5: \( b + f = 5.80 \), so \( b = 5.80 - f \) (Equation 2)

Step3: Substitute Equation 2 into Equation 1

Substitute \( b = 5.80 - f \) into \( 4b + 3f = 20.70 \):
\( 4(5.80 - f) + 3f = 20.70 \)
Expand: \( 23.20 - 4f + 3f = 20.70 \)
Simplify: \( 23.20 - f = 20.70 \)

Step4: Solve for \( f \)

Subtract 23.20 from both sides: \( -f = 20.70 - 23.20 = -2.50 \)
Multiply both sides by -1: \( f = 2.50 \)

Answer:

The cost for one order of fries is \$2.50.