If you know that 84 is 70% of the whole, how can you use proportional reasoning to determine the whole?


70100
shows 70% as a ratio. The ratio 84x
compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 120.


70100
shows 70% as a ratio. The ratio 84x
compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 58.8.


70100
shows 70% as a ratio. The ratio x84
compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.


70100
shows 70% as a ratio. The ratio x84
compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 58.8.

1 answer

To find the whole when it is known that 84 is 70% of it, you can set up a proportion based on the relationship between part and whole.

We know that:

\[ 70% = \frac{70}{100} \]

Let \( x \) be the whole. Thus, we can express the relationship as:

\[ \frac{84}{x} = \frac{70}{100} \]

To solve for \( x \), we can cross-multiply:

\[ 84 \cdot 100 = 70 \cdot x \]

This simplifies to:

\[ 8400 = 70x \]

Now, divide both sides by 70:

\[ x = \frac{8400}{70} = 120 \]

So, the whole is \( \boxed{120} \).