Question

the amount of water in a barrel decreased 9\frac{5}{8} pints in 7 weeks. the water decreased the same amount each week. what was the change in the amount of water in the barrel after 12 weeks?

Explanation:

Step1: Find weekly decrease

First, convert the mixed number \(9\frac{5}{8}\) to an improper fraction. \(9\frac{5}{8}=\frac{9\times8 + 5}{8}=\frac{77}{8}\) pints. The weekly decrease is \(\frac{77}{8}\div7\). Dividing by 7 is the same as multiplying by \(\frac{1}{7}\), so \(\frac{77}{8}\times\frac{1}{7}=\frac{11}{8}\) pints per week.

Step2: Calculate 12 - week decrease

Now, multiply the weekly decrease by 12. So, \(\frac{11}{8}\times12=\frac{11\times12}{8}=\frac{132}{8}=\frac{33}{2}=16\frac{1}{2}\) pints.

Answer:

The change in the amount of water after 12 weeks is \(16\frac{1}{2}\) pints (or \(\frac{33}{2}\) pints).