Question

1. a frozen yogurt shop has a combination of 150 small and medium sized bowls on their counter. each small bowl holds 4 ounces and each medium bowl holds 6 ounces. if the bowls on the counter will hold a total of 764 ounces, find the number of small and medium sized bowls on the counter.

Explanation:

Step1: Define variables

Let \( x \) be the number of small bowls and \( y \) be the number of medium bowls. We know two equations: \( x + y = 150 \) (total number of bowls) and \( 4x + 6y = 764 \) (total ounces).

Step2: Solve the first equation for \( x \)

From \( x + y = 150 \), we get \( x = 150 - y \).

Step3: Substitute into the second equation

Substitute \( x = 150 - y \) into \( 4x + 6y = 764 \): \( 4(150 - y) + 6y = 764 \).
Expand: \( 600 - 4y + 6y = 764 \).
Simplify: \( 600 + 2y = 764 \).
Subtract 600: \( 2y = 764 - 600 = 164 \).
Divide by 2: \( y = \frac{164}{2} = 82 \).

Step4: Find \( x \)

Substitute \( y = 82 \) into \( x = 150 - y \): \( x = 150 - 82 = 68 \).

Answer:

Small bowls: 68, Medium bowls: 82