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Problem 1

# There are 4 girls for every 7 boys in the swim club. Complete the following table with equivalent ratios: $$\begin{array}{|l|c|c|c|c|} \hline \text { Girls } & 4 & & 12 & \\ \hline \text { Boys } & 7 & 14 & & 28 \\ \hline \end{array}$$

Expert verified
The completed table with equivalent ratios is: $$\begin{array}{|l|c|c|c|c|} \hline \text { Girls } & 4 & 8 & 12 & \\ \hline \text { Boys } & 7 & 14 & 21 & 28 \\ \hline \end{array}$$
See the step by step solution

## Step 1: Ratio Recognition

Given in the exercise is a ratio of 4 girls for every 7 boys. This can be represented as the fraction $$\frac{4}{7}$$. Now, we need to keep the same proportion when completing the table with missing values.

## Step 2: Find the First Missing Value (Girls)

For the row with Boys numbers equal to 14, we have to keep the same proportion for the number of Girls in this case. We know that the ratio is $$\frac{4}{7}$$, so when the number of boys doubles to 14, we need to find the equivalent number of girls. Doubling the boys' value will require us to double the girls' value too, hence: $$2 \times 4 = 8$$ girls.

## Step 3: Find the Second Missing Value (Boys)

For the row with Girls numbers equal to 12, we have to keep the same proportion for the number of Boys in this case. We can first find out how many times more girls we have than in the original ratio: $$\frac{12}{4} = 3$$ Now, we'll do the same for the boys by multiplying the original Boys value by 3: $$3 \times 7 = 21$$ boys.

## Step 4: Fill the Completed Table

Now that we have found the missing values, we can fill in the completed table: $$\begin{array}{|l|c|c|c|c|} \hline \text { Girls } & 4 & 8 & 12 & \\ \hline \text { Boys } & 7 & 14 & 21 & 28 \\ \hline \end{array}$$ All equivalent ratios have been found, and the table is now complete.

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