Question

8 the amount of water in a barrel decreased 9^(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? 10 a horses weight decreases by 1/2 pound per week. at this rate how long will it take the horse to lose 5 1/2 pou write an expression that could be used to mode explain the strategy and/or tool that could be us

Explanation:

Problem 8:

Step 1: Convert mixed number to improper fraction

The total decrease in 7 weeks is \( 9\frac{5}{8} \) pints. Convert \( 9\frac{5}{8} \) to an improper fraction: \( 9\frac{5}{8}=\frac{9\times8 + 5}{8}=\frac{77}{8} \) pints.

Step 2: Find weekly decrease rate

To find the decrease per week, divide the total decrease by the number of weeks. So the weekly decrease is \( \frac{77}{8}\div7 \). Dividing by 7 is the same as multiplying by \( \frac{1}{7} \), so \( \frac{77}{8}\times\frac{1}{7}=\frac{11}{8} = 1\frac{3}{8} \) pints per week.

Step 3: Calculate decrease in 12 weeks

Now, to find the decrease in 12 weeks, multiply the weekly decrease by 12. So \( 1\frac{3}{8}\times12 \). Convert \( 1\frac{3}{8} \) to an improper fraction: \( \frac{11}{8} \). Then \( \frac{11}{8}\times12=\frac{11\times12}{8}=\frac{132}{8}=\frac{33}{2}=16\frac{1}{2} \) pints.

Step 1: Understand the rate and total loss

The horse loses \( \frac{1}{2} \) pound per week. We need to find the time \( t \) to lose \( 5\frac{1}{2} \) pounds.

Step 2: Set up the equation

The total loss is the rate times time, so \( \text{Total Loss}=\text{Rate}\times\text{Time} \). Let \( t \) be the time in weeks. So \( 5\frac{1}{2}=\frac{1}{2}\times t \).

Step 3: Solve for \( t \)

Convert \( 5\frac{1}{2} \) to an improper fraction: \( \frac{11}{2} \). Then \( \frac{11}{2}=\frac{1}{2}t \). Multiply both sides by 2: \( t = 11 \) weeks. The expression to model this is \( t=\frac{5\frac{1}{2}}{\frac{1}{2}} \) (or \( t=\frac{\frac{11}{2}}{\frac{1}{2}} \)). The strategy is using the formula \( \text{Time}=\frac{\text{Total Change}}{\text{Rate of Change}} \), where we divide the total weight to lose by the weekly weight loss rate.

Answer:

\( 16\frac{1}{2} \) pints (or \( \frac{33}{2} \) pints)

Problem 10:

(Assuming the question is to find the time to lose \( 5\frac{1}{2} \) pounds as the text seems cut off, but based on the given info)