Two hundred ten balloons are filled for a reception. This is 70 percent of the entire number of balloons purchased. Which equation can be used to find the total number of balloons purchased?

Question

A.StartFraction 210 divided by 3 Over 100 divided by 3 EndFraction = StartFraction 70 Over 33.3 EndFraction
B.StartFraction 70 times 3 Over 100 times 3 EndFraction = StartFraction 210 Over 300 EndFraction
C.StartFraction 100 divided by 3 Over 210 divided by 3 EndFraction = StartFraction 33.3 Over 70 EndFraction
D.StartFraction 70 times 3 Over 210 times 3 EndFraction = StartFraction 210 Over 630 EndFraction

Answer 1

To find the total number of balloons purchased, we know that 210 balloons represent 70 percent of the total.

Let \( x \) be the total number of balloons purchased. The relationship can be expressed as:

\[ 210 = 0.70 \times x \]

To solve for \( x \), we can rearrange the equation:

\[ x = \frac{210}{0.70} \]

Alternatively, we can express 0.70 as a fraction:

\[ x = \frac{210}{\frac{70}{100}} = 210 \times \frac{100}{70} = 210 \times \frac{10}{7} \]

This calculation shows how \( 210 \) and \( 70 \) relate to the total \( x \).

Now, let's analyze the provided options in that context:

• Option A: \( \frac{210}{3} = \frac{70}{33.3} \) - Not a correct representation of the relationship.
• Option B: \( \frac{70 \times 3}{100 \times 3} = \frac{210}{300} \) - This simplifies to \( \frac{70}{100} = \frac{210}{x} \), which reflects the same relationship correctly.
• Option C: \( \frac{100}{3} = \frac{33.3}{70} \) - Not a correct representation of the relationship.
• Option D: \( \frac{70 \times 3}{210 \times 3} = \frac{210}{630} \) - Not a correct representation of the relationship.

The correct equation that can be used to find the total number of balloons purchased is:

B. \(\frac{70 \times 3}{100 \times 3} = \frac{210}{300}\).