Question

tlaloc pumped up 56 balls. he pumped up 5 dodge balls for every 9 other balls.

complete the table.

\

$$\begin{tabular}{|l|c|c|} \\hline & original ratio & number tlaloc pumped up \\\\ \\hline dodge balls & 5 & \\\\ \\hline other balls & 9 & \\\\ \\hline total balls & & 56 \\\\ \\hline \\end{tabular}$$

Explanation:

🆕 New Concept Discovered: Ratios and Proportional Relationships
Using parts to find the whole and scaling up.

Step 1: Find the total in the original ratio

The original ratio of dodge balls to other balls is \(5:9\).

To find the total parts in this original ratio group, add the two parts together:

$$5 + 9 = 14$$

So, the original total balls box is 14.

Step 2: Determine the scaling factor

We know the actual total number of balls Tlaloc pumped up is \(56\).

To find how many times larger the actual total is compared to our ratio total, divide the actual total by the ratio total:

$$\frac{56}{14} = 4$$

This means we need to multiply each part of the original ratio by \(4\) to find the actual numbers.

Step 3: Calculate the actual number of each type of ball

Multiply the original ratio values by the scaling factor of \(4\):

• Dodge balls:

$$5 \times 4 = 20$$

• Other balls:

$$9 \times 4 = 36$$

Answer:

• Total balls (Original ratio): 14
• Dodge balls (Number Tlaloc pumped up): 20
• Other balls (Number Tlaloc pumped up): 36