Question

intro to percents

1. what percent of 88 is 33?
2. what number is 69% of 840?
3. 120% of what number is 54?
4. 19 is what percent of 95?

Explanation:

Problem 4: What percent of 88 is 33?

Step1: Set up the percent formula

Let the percent be \( x \). The formula for "what percent of \( a \) is \( b \)" is \( \frac{b}{a} = \frac{x}{100} \). Here, \( a = 88 \) and \( b = 33 \), so we have \( \frac{33}{88} = \frac{x}{100} \).

Step2: Solve for \( x \)

First, simplify \( \frac{33}{88} = \frac{3}{8} \). Then, cross - multiply: \( 8x = 3\times100 \), so \( 8x = 300 \). Then \( x=\frac{300}{8}=37.5 \).

Step1: Recall the percent formula

The formula for "what number is \( p\% \) of \( a \)" is \( n = p\%\times a \). Here, \( p = 65 \) and \( a = 840 \), so \( n = 0.65\times840 \).

Step2: Calculate the product

\( 0.65\times840=(0.6 + 0.05)\times840=0.6\times840+0.05\times840 = 504+42 = 546 \).

Step1: Set up the equation

Let the number be \( x \). The formula for " \( p\% \) of \( x \) is \( n \)" is \( p\%\times x=n \). Here, \( p = 120 \), \( n = 54 \), so \( 1.2x = 54 \).

Step2: Solve for \( x \)

Divide both sides of the equation by \( 1.2 \): \( x=\frac{54}{1.2}=45 \).

Answer:

\( 37.5\% \)

Problem 6: What number is 65% of 840?