Question

1. which of the following proportions could be used to find, “42 is 35% of what number?” a. $\frac{35}{100}=\frac{x}{42}$ c. $\frac{x}{35}=\frac{42}{100}$ b. $\frac{35}{x}=\frac{42}{100}$ d. $\frac{35}{100}=\frac{42}{x}$ 2. what does the shaded portion represent? fraction: __ decimal: percent: __ use your understanding of percent proportions and percent equations to solve the questions below. 3. 36 is 30% of what number? 4. what percent of 88 is 33? 5. what number is 65% of 840? 6. what is 125% of 64? 7. 120% of what number is 54? 8. 19 is what percent of 95? 9. mr. glover wrote the problem, “find 16% of 50” on the whiteboard and asked students to create a proportion or equation to solve the problem. circle the name of anyone who made a true statement. maxine i can use the proportion $\frac{x}{50}=\frac{16}{100}$ to solve. theo i can find 16% because i can divide 50 by 16. bryan i know that 16% of 50 is going to be less than 10, because 10% is 5 and 20% is 10. elaine i can change 16% to 1.6 and multiply it by 50.

Explanation:

Step1: Recall percent - proportion formula

The percent - proportion formula is $\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}$. In the statement “42 is 35% of what number?”, 42 is the part, 35 is the percent, and the unknown number is the whole. Let the unknown number be $x$. Then the proportion is $\frac{35}{100}=\frac{42}{x}$, so the answer to question 1 is d.

Step2: Analyze the shaded portion

There are 10 equal - sized rectangles, and 8 are shaded. The fraction of the shaded portion is $\frac{8}{10}=\frac{4}{5}$. The decimal is $0.8$ (since $8\div10 = 0.8$), and the percent is $80\%$ (since $0.8\times100 = 80$).

Step3: Solve “36 is 30% of what number?”

Using the formula $\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}$, let the whole be $x$. We have $\frac{30}{100}=\frac{36}{x}$. Cross - multiply: $30x=36\times100$, so $30x = 3600$. Then $x=\frac{3600}{30}=120$.

Step4: Solve “What percent of 88 is 33?”

Let the percent be $p$. The proportion is $\frac{p}{100}=\frac{33}{88}$. Cross - multiply: $88p=33\times100$, so $88p = 3300$. Then $p=\frac{3300}{88}=37.5$.

Step5: Solve “What number is 65% of 840?”

Using the formula $\text{part}=\text{percent}\times\text{whole}$, convert 65% to a decimal ($0.65$). Then the part is $0.65\times840 = 546$.

Step6: Solve “What is 125% of 64?”

Convert 125% to a decimal ($1.25$). Then $1.25\times64=(1 + 0.25)\times64=64+0.25\times64=64 + 16=80$.

Step7: Solve “120% of what number is 54?”

Let the number be $x$. The equation is $1.2x = 54$. Then $x=\frac{54}{1.2}=45$.

Step8: Solve “19 is what percent of 95?”

Let the percent be $p$. The proportion is $\frac{p}{100}=\frac{19}{95}$. Cross - multiply: $95p=19\times100$, so $95p = 1900$. Then $p=\frac{1900}{95}=20$.

Step9: Analyze the students' statements

For “Find 16% of 50”:
Maxine's proportion $\frac{x}{50}=\frac{16}{100}$ is correct. Theo's method of dividing 50 by 16 is incorrect. Bryan's reasoning about the value range is correct but not a proportion or equation to solve. Elaine's conversion of 16% to 1.6 is incorrect (16% should be 0.16). So circle Maxine.

Answer:

1. d. $\frac{35}{100}=\frac{42}{x}$
2. fraction: $\frac{4}{5}$; decimal: $0.8$; percent: $80\%$
3. 120
4. 37.5
5. 546
6. 80
7. 45
8. 20
9. Maxine