7th Grade Common Core Math Worksheets - Free Printable

Problem Set: Solving Problems with Unknown Base or Percent

We will solve each problem step by step, explaining the reasoning and calculations.

---

#### Problem 1:
The table shows responses to a survey of registered voters.
| Candidate | Registered Voters Planning to Vote for Candidate |
|-----------|--------------------------------------------------|
| Warren | 329 |
| Largo | 462 |
| Fredricks | 264 |

Find the sample proportion for voters favoring Fredricks as a decimal and as a percent.

Solution:
1. Total number of voters surveyed:
\[
\text{Total} = 329 + 462 + 264 = 1055
\]

2. Number of voters favoring Fredricks:
\[
\text{Voters for Fredricks} = 264
\]

3. Proportion of voters favoring Fredricks:
\[
\text{Proportion} = \frac{\text{Voters for Fredricks}}{\text{Total voters}} = \frac{264}{1055}
\]

4. Calculate the decimal:
\[
\frac{264}{1055} \approx 0.2502
\]

5. Convert to a percent:
\[
0.2502 \times 100 \approx 25.0\%
\]

Answer:
\[
\boxed{0.250 \text{ (decimal)}, 25.0\% \text{ (percent)}}
\]

---

#### Problem 2:
In 1994, there were 60,239,000 women in the civilian labor force. Of those women, 3,585,000 were 16 to 19 years of age. What percent of the women in the labor force were 20 years or older?

Solution:
1. Total number of women in the labor force:
\[
\text{Total} = 60,239,000
\]

2. Number of women aged 16 to 19:
\[
\text{Aged 16 to 19} = 3,585,000
\]

3. Number of women aged 20 or older:
\[
\text{Aged 20 or older} = \text{Total} - \text{Aged 16 to 19} = 60,239,000 - 3,585,000 = 56,654,000
\]

4. Proportion of women aged 20 or older:
\[
\text{Proportion} = \frac{\text{Aged 20 or older}}{\text{Total}} = \frac{56,654,000}{60,239,000}
\]

5. Calculate the decimal:
\[
\frac{56,654,000}{60,239,000} \approx 0.9405
\]

6. Convert to a percent:
\[
0.9405 \times 100 \approx 94.05\%
\]

Answer:
\[
\boxed{94.05\%}
\]

---

#### Problem 3:
In 1992, U.S. farmers produced 240,774,000 metric tons of corn. Suppose a farmer produced 1,655,000 metric tons of corn. What percent of the 1992 U.S. corn production did the farmer raise? Round your answer to the nearest tenth of a percent.

Solution:
1. Total corn production in 1992:
\[
\text{Total} = 240,774,000 \text{ metric tons}
\]

2. Corn production by the farmer:
\[
\text{Farmer's production} = 1,655,000 \text{ metric tons}
\]

3. Proportion of corn production by the farmer:
\[
\text{Proportion} = \frac{\text{Farmer's production}}{\text{Total}} = \frac{1,655,000}{240,774,000}
\]

4. Calculate the decimal:
\[
\frac{1,655,000}{240,774,000} \approx 0.00687
\]

5. Convert to a percent:
\[
0.00687 \times 100 \approx 0.687\%
\]

6. Round to the nearest tenth of a percent:
\[
0.687\% \approx 0.7\%
\]

Answer:
\[
\boxed{0.7\%}
\]

---

#### Problem 4:
A survey showed that 56% of car owners prefer four-door cars, 31% prefer two-door cars, and 13% have no preference. You ask 500 people. How many do you think will prefer four-door cars?

Solution:
1. Percentage of car owners who prefer four-door cars:
\[
56\%
\]

2. Total number of people surveyed:
\[
500
\]

3. Number of people who prefer four-door cars:
\[
\text{Number} = \text{Percentage} \times \text{Total} = 0.56 \times 500
\]

4. Calculate the number:
\[
0.56 \times 500 = 280
\]

Answer:
\[
\boxed{280}
\]

---

#### Problem 5:
In a random selection, 25% of the people polled preferred talk radio. If a total of 119 people polled preferred talk radio, how many people were polled?

Solution:
1. Percentage of people who preferred talk radio:
\[
25\% = 0.25
\]

2. Number of people who preferred talk radio:
\[
119
\]

3. Let \( x \) be the total number of people polled.
\[
0.25 \times x = 119
\]

4. Solve for \( x \):
\[
x = \frac{119}{0.25} = 476
\]

Answer:
\[
\boxed{476}
\]

---

#### Problem 6:
In a random selection, 40% of the people polled preferred the music of Mozart. If a total of 238 people polled preferred the music of Mozart, how many people were polled?

Solution:
1. Percentage of people who preferred Mozart:
\[
40\% = 0.40
\]

2. Number of people who preferred Mozart:
\[
238
\]

3. Let \( x \) be the total number of people polled.
\[
0.40 \times x = 238
\]

4. Solve for \( x \):
\[
x = \frac{238}{0.40} = 595
\]

Answer:
\[
\boxed{595}
\]

---

#### Problem 7:
In a random selection, 20% of the people polled preferred Brand A. If a total of 119 people polled preferred Brand A, how many people were polled?

Solution:
1. Percentage of people who preferred Brand A:
\[
20\% = 0.20
\]

2. Number of people who preferred Brand A:
\[
119
\]

3. Let \( x \) be the total number of people polled.
\[
0.20 \times x = 119
\]

4. Solve for \( x \):
\[
x = \frac{119}{0.20} = 595
\]

Answer:
\[
\boxed{595}
\]

---

#### Problem 8:
A golf group planned a trip to Hawaii and 7 of the members signed up to go. If this is 10% of the club, how many members does the golf group have in total?

Solution:
1. Percentage of members who signed up:
\[
10\% = 0.10
\]

2. Number of members who signed up:
\[
7
\]

3. Let \( x \) be the total number of members in the golf group.
\[
0.10 \times x = 7
\]

4. Solve for \( x \):
\[
x = \frac{7}{0.10} = 70
\]

Answer:
\[
\boxed{70}
\]

---

#### Problem 9:
A ski club planned a trip to Lake Tahoe and 24 of the members signed up to go. If this is 20% of the club, how many members does the ski club have in total?

Solution:
1. Percentage of members who signed up:
\[
20\% = 0.20
\]

2. Number of members who signed up:
\[
24
\]

3. Let \( x \) be the total number of members in the ski club.
\[
0.20 \times x = 24
\]

4. Solve for \( x \):
\[
x = \frac{24}{0.20} = 120
\]

Answer:
\[
\boxed{120}
\]

---

#### Problem 10:
A golf group planned a trip to Palm Springs and 96 of the members signed up to go. If this is 60% of the club, how many members does the golf group have in total?

Solution:
1. Percentage of members who signed up:
\[
60\% = 0.60
\]

2. Number of members who signed up:
\[
96
\]

3. Let \( x \) be the total number of members in the golf group.
\[
0.60 \times x = 96
\]

4. Solve for \( x \):
\[
x = \frac{96}{0.60} = 160
\]

Answer:
\[
\boxed{160}
\]

---

Final Answers:

1. \(\boxed{0.250 \text{ (decimal)}, 25.0\% \text{ (percent)}}\)
2. \(\boxed{94.05\%}\)
3. \(\boxed{0.7\%}\)
4. \(\boxed{280}\)
5. \(\boxed{476}\)
6. \(\boxed{595}\)
7. \(\boxed{595}\)
8. \(\boxed{70}\)
9. \(\boxed{120}\)
10. \(\boxed{160}\)