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

StartFraction 210 divided by 3 Over 100 divided by 3 EndFraction = StartFraction 70 Over 33.3 EndFraction
StartFraction 70 times 3 Over 100 times 3 EndFraction = StartFraction 210 Over 300 EndFraction
StartFraction 100 divided by 3 Over 210 divided by 3 EndFraction = StartFraction 33.3 Over 70 EndFraction
StartFraction 70 times 3 Over 210 times 3 EndFraction = StartFraction 210 Over 630 EndFraction

Answer 1

To find the total number of balloons purchased based on the information that 210 balloons represent 70 percent of that total, we can set up the following relationship:

Let \( x \) be the total number of balloons purchased. Since 70 percent of \( x \) is equal to 210, we write the equation:

\[ 0.7x = 210 \]

Rewriting the equation gives us:

\[ x = \frac{210}{0.7} \]

Now, let's analyze the fractions provided in your options:

1. \( \frac{210/3}{100/3} = \frac{70}{33.3} \)
2. \( \frac{70 \times 3}{100 \times 3} = \frac{210}{300} \)
3. \( \frac{100/3}{210/3} = \frac{33.3}{70} \)
4. \( \frac{70 \times 3}{210 \times 3} = \frac{210}{630} \)

Option 2 simplifies to \( \frac{70}{100} = \frac{210}{300} \), which is equivalent and correct but does not directly establish a clear equation for solving for the total number.

None of the options neatly convert into \( 0.7x = 210 \) or a rearrangement of that relationship.

However, the most relevant fraction is:

\[ \frac{70 \times 3}{100 \times 3} = \frac{210}{300} \]

This indicates that 70% is represented correctly when relating 210 to the equivalent fraction based on 100% being 300.

Thus, the best option among those provided for finding the total number of balloons purchased is:

\[ \frac{70 \times 3}{100 \times 3} = \frac{210}{300} \]

This means the total number of balloons purchased is 300 (where 210 is 70% of that total).