Let's solve each of the word problems step by step.
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Problem 1:
The cable bill is normally $83.47 a month. This month the bill will be increased by 12%. Based on the new price, what will the cable bill cost for a year?
#### Step 1: Calculate the 12% increase
Increase = 12% of $83.47
= 0.12 × 83.47
= $10.0164
#### Step 2: Find the new monthly bill
New monthly bill = $83.47 + $10.0164 = $93.4864
(Rounded to the nearest cent:
$93.49)
#### Step 3: Calculate the yearly cost
Yearly cost = $93.49 × 12 =
$1,121.88
✔ Answer: The cable bill will cost
$1,121.88 for a year.
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Problem 2:
You will measure 73 ½ inches wide. You want to place a picture in the center of the wall. How far from the wall edge should you place the nail?
We assume the wall is wide enough that the picture is centered horizontally.
- Width of picture = 73.5 inches
- To center it, we divide the width by 2 to find the distance from the edge to the center.
Distance from edge = 73.5 ÷ 2 =
36.75 inches
✔ Answer: Place the nail
36.75 inches (or
36 ¾ inches) from the wall edge.
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Problem 3:
You use 1,500 gallons of oil every year to heat your home. Last year you paid $4,650 for all your oil. You add a regulator to your furnace that is guaranteed to make the furnace use 15% less oil. If you pay the same rate per gallon, how much do you expect to pay each month?
#### Step 1: Find the original cost per gallon
Total cost = $4,650
Total oil used = 1,500 gallons
Cost per gallon = $4,650 ÷ 1,500 =
$3.10 per gallon
#### Step 2: New oil usage with 15% reduction
Reduction = 15% of 1,500 = 0.15 × 1,500 = 225 gallons
New oil usage = 1,500 - 225 =
1,275 gallons per year
#### Step 3: New total cost
New cost = 1,275 × $3.10 =
$3,942.50 per year
#### Step 4: Monthly cost
Monthly cost = $3,942.50 ÷ 12 =
$328.54
✔ Answer: You expect to pay
$328.54 per month.
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Problem 4:
You need to have your car’s oil changed every 3,500 miles. An oil change costs $42.00 + tax at 2.5%. You drive 14,000 miles every year. How much will oil change costs you over a year?
#### Step 1: How many oil changes per year?
Miles driven per year = 14,000
Oil change interval = 3,500 miles
Number of oil changes = 14,000 ÷ 3,500 =
4 oil changes per year
#### Step 2: Cost per oil change including tax
Tax = 2.5% of $42.00 = 0.025 × 42 = $1.05
Total cost per oil change = $42.00 + $1.05 =
$43.05
#### Step 3: Total annual cost
Total cost = 4 × $43.05 =
$172.20
✔ Answer: Oil change costs will be
$172.20 over a year.
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✔ Final Answers:
1.
$1,121.88
2.
36.75 inches (or
36 ¾ inches)
3.
$328.54 per month
4.
$172.20 per year
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Parent Tip: Review the logic above to help your child master the concept of 7th grade algebra word problems worksheet.
