Which equation can be used to solve the problem?

Question

75 percent of what number is 150?
StartFraction 75 times 1 Over 150 times 1 EndFraction = StartFraction 75 Over 150 EndFraction
StartFraction 150 times 2 Over 75 times 2 EndFraction = StartFraction 300 Over 150 EndFraction
StartFraction 200 times 2 Over 75 times 2 EndFraction = StartFraction 400 Over 150 EndFraction
StartFraction 75 times 2 Over 100 times 2 EndFraction = StartFraction 150 Over 200 EndFraction but make it simple

Answer 1

To solve the problem, "75 percent of what number is 150?", we can express it as an equation.

Let \( x \) be the unknown number. The equation can be written as:

\[ 0.75x = 150 \]

To solve for \( x \), you divide both sides by 0.75:

\[ x = \frac{150}{0.75} \]

This equation effectively captures the problem of finding the number from which 75 percent equals 150.

If we wish to convert it to a simpler form without decimals, we can rewrite 75% as a fraction:

\[ \frac{75}{100}x = 150 \]

Then we can simplify \( \frac{75}{100} \) to \( \frac{3}{4} \):

\[ \frac{3}{4}x = 150 \]

To eliminate the fraction, multiply both sides by 4:

\[ 3x = 600 \]

Finally, divide by 3:

\[ x = 200 \]

Thus, the number is 200. The original equation that could be used to solve the problem is:

\[ 0.75x = 150 \]

or, in fraction form:

\[ \frac{3}{4}x = 150 \]