7th Grade Math Problems: Complete with ease | airSlate SignNow - Free Printable

Problem 1: Cable Bill Cost for a Year

Question: The cable bill is normally $83.47 per month. This month, the bill will be increased by 12%. Based on the new price, what will the cable bill cost for a year?

#### Solution:
1. Calculate the new monthly bill after a 12% increase:
- Original monthly bill = $83.47
- Increase percentage = 12% = 0.12
- New monthly bill = Original bill + (Original bill × Increase percentage)
\[
\text{New monthly bill} = 83.47 + (83.47 \times 0.12)
\]
\[
\text{New monthly bill} = 83.47 + 10.0164 = 93.4864
\]
Round to two decimal places: $93.49

2. Calculate the annual bill:
- Number of months in a year = 12
- Annual bill = New monthly bill × 12
\[
\text{Annual bill} = 93.49 \times 12 = 1121.88
\]

#### Final Answer:
\[
\boxed{1121.88}
\]

---

Problem 2: Placing a Picture on the Wall

Question: The wall measures 73 ½ inches wide. You want to place a picture in the center of the wall. How far from the left edge should you place the nail?

#### Solution:
1. Understand the problem:
- The wall is 73 ½ inches wide.
- To center the picture, the distance from the left edge to the center of the picture must be half the width of the wall.

2. Calculate half the width of the wall:
- Width of the wall = 73 ½ inches = 73.5 inches
- Half the width = \( \frac{73.5}{2} \)
\[
\text{Half the width} = 36.75 \text{ inches}
\]

3. Conclusion:
- The nail should be placed 36.75 inches from the left edge to center the picture.

#### Final Answer:
\[
\boxed{36.75}
\]

---

Problem 3: Oil Bill with Regulator

Question: You use 1,500 gallons of oil every year to heat your home. Last year, you paid $4,650 for oil. You add a regulator that is guaranteed to make the furnace use 15% less oil. If you pay the oil bill monthly, how much do you expect to pay each month?

#### Solution:
1. Calculate the cost per gallon of oil last year:
- Total oil used last year = 1,500 gallons
- Total cost last year = $4,650
- Cost per gallon = \( \frac{\text{Total cost}}{\text{Total gallons}} \)
\[
\text{Cost per gallon} = \frac{4650}{1500} = 3.10 \text{ dollars per gallon}
\]

2. Calculate the reduced oil usage with the regulator:
- Reduction in oil usage = 15% = 0.15
- Reduced oil usage = Original usage × (1 - Reduction percentage)
\[
\text{Reduced oil usage} = 1500 \times (1 - 0.15) = 1500 \times 0.85 = 1275 \text{ gallons}
\]

3. Calculate the total cost with the regulator:
- Cost per gallon = $3.10
- Total cost with regulator = Reduced oil usage × Cost per gallon
\[
\text{Total cost with regulator} = 1275 \times 3.10 = 3952.50 \text{ dollars}
\]

4. Calculate the monthly oil bill:
- Number of months in a year = 12
- Monthly bill = Total cost with regulator ÷ 12
\[
\text{Monthly bill} = \frac{3952.50}{12} = 329.375
\]
Round to two decimal places: $329.38

#### Final Answer:
\[
\boxed{329.38}
\]

---

Problem 4: Car Oil Change Costs

Question: You need to have your car's oil changed every 3,500 miles. An oil change costs $42.80 + tax at 8.25%. If you drive 14,000 miles every year, how much will oil changes cost you over a year?

#### Solution:
1. Calculate the number of oil changes per year:
- Miles driven per year = 14,000 miles
- Miles between oil changes = 3,500 miles
- Number of oil changes per year = \( \frac{\text{Miles driven per year}}{\text{Miles between oil changes}} \)
\[
\text{Number of oil changes per year} = \frac{14000}{3500} = 4
\]

2. Calculate the cost of one oil change including tax:
- Cost of oil change before tax = $42.80
- Tax rate = 8.25% = 0.0825
- Tax amount = Cost before tax × Tax rate
\[
\text{Tax amount} = 42.80 \times 0.0825 = 3.537
\]
Round to two decimal places: $3.54
- Total cost of one oil change = Cost before tax + Tax amount
\[
\text{Total cost of one oil change} = 42.80 + 3.54 = 46.34
\]

3. Calculate the total cost for all oil changes in a year:
- Number of oil changes per year = 4
- Total cost per year = Cost of one oil change × Number of oil changes
\[
\text{Total cost per year} = 46.34 \times 4 = 185.36
\]

#### Final Answer:
\[
\boxed{185.36}
\]

---

Summary of Answers:

1. \(\boxed{1121.88}\)
2. \(\boxed{36.75}\)
3. \(\boxed{329.38}\)
4. \(\boxed{185.36}\)