Question

Alana's cat weighs 8 1/2 pounds. Alana's dog weighs 8 5/6 times as much as her cat. How much does Alana's dog weigh?

Write your answer as a fraction or as a whole or mixed number.

pounds

Answer 1

To find out how much Alana's dog weighs, we start by calculating the dog's weight as a multiple of the cat's weight.

1. First, we convert Alana's cat's weight into an improper fraction. The cat weighs \(8 \frac{1}{2}\) pounds:
\[
8 \frac{1}{2} = \frac{17}{2} \text{ pounds}
\]

2. Next, we need to calculate the weight of Alana's dog, which is \(8 \frac{5}{6}\) times the weight of the cat:
\[
\text{Dog's weight} = \frac{8}{1} \times \frac{17}{2} \times \frac{5}{6}
\]

To handle the multiplication, we can first express \(8\) as a fraction:
\[
8 = \frac{8}{1}
\]

Now multiply:
\[
\frac{8}{1} \times \frac{17}{2} = \frac{8 \times 17}{1 \times 2} = \frac{136}{2} = 68
\]

Now multiply that by \(\frac{5}{6}\):
\[
68 \times \frac{5}{6} = \frac{68 \times 5}{6} = \frac{340}{6}
\]

3. Now, simplify \(\frac{340}{6}\):
\[
\frac{340 \div 2}{6 \div 2} = \frac{170}{3}
\]

4. To express \(\frac{170}{3}\) as a mixed number, we perform the division:
\[
170 \div 3 = 56 \quad \text{remainder } 2
\]
Thus, we can write:
\[
\frac{170}{3} = 56 \frac{2}{3}
\]

Therefore, Alana's dog weighs \(\boxed{56 \frac{2}{3}}\) pounds.