Question

yolanda, ryan, and manuel served a total of 113 orders monday at the school cafeteria. manuel served 7 more orders than yolanda. ryan served 4 times as many orders as manuel. how many orders did they each serve?
number of orders yolanda served:
number of orders ryan served:
number of orders manuel served:

Explanation:

Step1: Define variables

Let the number of orders Yolanda served be \( y \). Then Manuel served \( y + 7 \) orders, and Ryan served \( 4(y + 7) \) orders. The total orders served is 113, so we set up the equation: \( y+(y + 7)+4(y + 7)=113 \).

Step2: Simplify the equation

First, expand the terms: \( y + y + 7+4y + 28 = 113 \). Then combine like terms: \( 6y+35 = 113 \).

Step3: Solve for \( y \)

Subtract 35 from both sides: \( 6y=113 - 35=78 \). Then divide by 6: \( y=\frac{78}{6}=13 \).

Step4: Find orders for each

• Yolanda: \( y = 13 \)
• Manuel: \( y + 7=13 + 7 = 20 \)
• Ryan: \( 4\times20 = 80 \) (Check: \( 13+20+80 = 113 \), which matches the total.)

Answer:

Yolanda served 13 orders, Manuel served 20 orders, Ryan served 80 orders.