Percent: Additional Practice (Set 2)

The part is $54$ and the percent is $72$, with the whole unknown. Set up $\frac{54}{w} = \frac{72}{100}$, multiply the known diagonal $54 \times 100$, and divide by $72$.

$w = \frac{54 \times 100}{72} = \frac{5400}{72} = 75$

Check: $72\%$ of $75$ is $0.72 \times 75 = 54$.

The part is $42$ and the whole is $120$. Set up $\frac{42}{120} = \frac{p}{100}$, cross-multiply, and divide by $120$.

$p = \frac{42 \times 100}{120} = \frac{4200}{120} = 35$

So $42$ is $35\%$ of $120$.

The part is $33$ and the percent is $44$. Set up $\frac{33}{w} = \frac{44}{100}$, multiply the known diagonal $33 \times 100$, and divide by $44$.

$w = \frac{33 \times 100}{44} = \frac{3300}{44} = 75$

Check: $44\%$ of $75$ is $0.44 \times 75 = 33$.

Convert to a decimal and multiply.

$4\% = 0.04 \;\Rightarrow\; 0.04 \times 325 = 13$

So $4\%$ of $325$ is $13$.

Convert to a decimal and multiply. Note that $2.5\% = 0.025$.

$0.025 \times 800 = 20$

So $2.5\%$ of $800$ is $20$.

Convert to a decimal and multiply.

$16\% = 0.16 \;\Rightarrow\; 0.16 \times 150 = 24$

So $16\%$ of $150$ is $24$.

The part is $84$ and the percent is $120$. Since the percent is above $100$, the whole is smaller than the part. Set up $\frac{84}{w} = \frac{120}{100}$, multiply the known diagonal $84 \times 100$, and divide by $120$.

$w = \frac{84 \times 100}{120} = \frac{8400}{120} = 70$

Check: $120\%$ of $70$ is $1.2 \times 70 = 84$.

The $45$ liters are the part and $30$ is the percent, with the full capacity unknown. Set up $\frac{45}{w} = \frac{30}{100}$, multiply the known diagonal $45 \times 100$, and divide by $30$.

$w = \frac{45 \times 100}{30} = \frac{4500}{30} = 150$

So the tank holds $150$ liters when full.

Convert to a decimal and multiply.

$6\% = 0.06 \;\Rightarrow\; 0.06 \times 75 = 4.5$

So $6\%$ of $75$ is $4.5$.

The part is $22$ and the percent is $55$. Set up $\frac{22}{w} = \frac{55}{100}$, multiply the known diagonal $22 \times 100$, and divide by $55$.

$w = \frac{22 \times 100}{55} = \frac{2200}{55} = 40$

Check: $55\%$ of $40$ is $0.55 \times 40 = 22$.

The part is $7$ and the whole is $200$. Set up $\frac{7}{200} = \frac{p}{100}$, cross-multiply, and divide by $200$.

$p = \frac{7 \times 100}{200} = \frac{700}{200} = 3.5$

So $7$ is $3.5\%$ of $200$.

Convert to a decimal and multiply.

$45\% = 0.45 \;\Rightarrow\; 0.45 \times 120 = 54$

So $45\%$ of $120$ is $54$.