Certainly! Let's solve each of the equations step by step, and then we'll address the percentage questions.
### Section 3: Single Step Equations
1. Solve [tex]\(4 + b = 30\)[/tex]:
- To isolate [tex]\(b\)[/tex], subtract 4 from both sides:
[tex]\[
b = 30 - 4
\][/tex]
- Therefore:
[tex]\[
b = 26
\][/tex]
2. Solve [tex]\(r - 18 = 27\)[/tex]:
- To isolate [tex]\(r\)[/tex], add 18 to both sides:
[tex]\[
r = 27 + 18
\][/tex]
- Therefore:
[tex]\[
r = 45
\][/tex]
3. Solve [tex]\(2x = 16\)[/tex]:
- To isolate [tex]\(x\)[/tex], divide both sides by 2:
[tex]\[
x = \frac{16}{2}
\][/tex]
- Therefore:
[tex]\[
x = 8
\][/tex]
4. Solve [tex]\(\frac{k}{2} = 6\)[/tex]:
- To isolate [tex]\(k\)[/tex], multiply both sides by 2:
[tex]\[
k = 6 \times 2
\][/tex]
- Therefore:
[tex]\[
k = 12
\][/tex]
5. Solve [tex]\(6p = 30\)[/tex]:
- To isolate [tex]\(p\)[/tex], divide both sides by 6:
[tex]\[
p = \frac{30}{6}
\][/tex]
- Therefore:
[tex]\[
p = 5
\][/tex]
### Section 4: Percents
1. 48 is what percent of 75?:
- To find the percentage, use the formula:
[tex]\[
\text{Percent} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100
\][/tex]
- Substituting the values:
[tex]\[
\text{Percent} = \left( \frac{48}{75} \right) \times 100
\][/tex]
- Therefore:
[tex]\[
\text{Percent} \approx 64.0\%
\][/tex]
2. What percent of 25 is 15?:
- Using the same formula:
[tex]\[
\text{Percent} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100
\][/tex]
- Substituting the values:
[tex]\[
\text{Percent} = \left( \frac{15}{25} \right) \times 100
\][/tex]
- Therefore:
[tex]\[
\text{Percent} = 60.0\%
\][/tex]
### Summary of Solutions:
1. [tex]\( b = 26 \)[/tex]
2. [tex]\( r = 45 \)[/tex]
3. [tex]\( x = 8 \)[/tex]
4. [tex]\( k = 12 \)[/tex]
5. [tex]\( p = 5 \)[/tex]
6. 48 is [tex]\( 64.0\% \)[/tex] of 75.
7. 15 is [tex]\( 60.0\% \)[/tex] of 25.
I hope this detailed solution helps you understand how each step is done!
