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Math  /  Numbers & Operations

QuestionGreta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Last week, Greta fed Draco 77 crickets.
How many crickets did Greta feed Lizzy? □\square crickets

Studdy Solution

STEP 1

1. The ratio of crickets fed to Draco and Lizzy is 11 11 to 8 8 .
2. Greta fed Draco 77 77 crickets last week.
3. We need to determine how many crickets Greta fed Lizzy last week.

STEP 2

1. Define the variable
2. Set up a proportion.
3. Solve the proportion.

STEP 3

Let y y be the number of crickets Greta fed Lizzy.

STEP 4

Start with a mix of words and symbols to ensure the proportion is set up correctly.
11 crickets to Draco8 crickets to Lizzy=77 crickets to Dracoy crickets to Lizzy\frac{11 \text{ crickets to Draco}}{8 \text{ crickets to Lizzy}} = \frac{77 \text{ crickets to Draco}}{y \text{ crickets to Lizzy}}

STEP 5

Write the proportion.
118=77y \frac{11}{8} = \frac{77}{y}

STEP 6

Multiply both sides by y y to isolate y y .
118=77y \frac{11}{8} = \frac{77}{y} y(118)=77 y\left(\frac{11}{8}\right) = 77 y=77×811 y = \frac{77 \times 8}{11}

STEP 7

Calculate the number of crickets fed to Lizzy:
y=77×811=61611=56 y = \frac{77 \times 8}{11} = \frac{616}{11} = 56
The number of crickets Greta fed Lizzy is:
56 crickets\boxed{56 \text{ crickets}}

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