In some problems, the question is not simply, "What is the value of the part." Sometimes you need to find a new total.
Let's take a look at the clearance sale example from section 2 again:
A store is holding a clearance sale with everything to be sold at 25% off the regular price. If the original price of an item is $20.00, how much will you save? (Answer: $5.00)
Another question that could be asked is: "Now, how much will you pay?"
Answer the following questions to help analyze this situation.
Is the price going up because of the sale or is the price going down because of the sale?
Interactive popup. Assistance may be required. The price is going down.
Knowing the amount saved, what mathematical operation should you use to find the new price that you will pay?
Interactive popup. Assistance may be required. Subtraction
Write a plan for finding the new price:
Interactive popup. Assistance may be required. To find the new price, you need to subtract the amount you save from the original price.
Write your plan as an equation solving for S, the sale price.
Interactive popup. Assistance may be required. S = 20 – 5
What is the sale price?
Interactive popup. Assistance may be required. S = 15
Now, let's take a look at the clearance sale example from section 2 again.
Your parents decide to paint the living room. When they go to the paint store, they find that they need to buy $75.00 worth of paint. If the sales tax rate is 8%, how much money will be added to the price of the paint? (Answer: $6.00)
The problem could have asked, "How much will your parents have to pay for the paint including tax?"
Is the total going up because of the tax, or is the total going down because of the tax?
Interactive popup. Assistance may be required. The total is going up.
What mathematical operation should you use to find the total cost of the paint with tax?
Interactive popup. Assistance may be required. Addition
Write a plan for finding the total cost of the paint including tax:
Interactive popup. Assistance may be required. To find the total cost, you need to add the sales tax to the price of the paint.
Write your plan as an equation solving for C, the total cost.
Interactive popup. Assistance may be required. C = 75 + 6
What is the total cost?
Interactive popup. Assistance may be required. C = 81
Based on these two example problems, how do you find the new total when you are given a percent increase or decrease?
Interactive popup. Assistance may be required. You need to use the percent to find how much the total changes (the part), and then add or subtract that with the original total (the whole).
How do you know if you should add or subtract?
Interactive popup. Assistance may be required. It depends on whether the problem says the amount is going up (add) or down (subtract).
The population of a small town is growing at 5% per year. In 2010 the population was 15,000 people. What will the new population be in 2011 if the rate of growth stays at 5%?
What is the change in population?
Interactive popup. Assistance may be required. Change in population = 0.05 (15000)
What was the value of the original population?
Interactive popup. Assistance may be required. The original population = 15000 people
Should you add or subtract?
Interactive popup. Assistance may be required. You need to add.
How did you know?
Interactive popup. Assistance may be required. The population is growing.
What is the new population?
Interactive popup. Assistance may be required. New population = 15000 + 750