~ 4.8 ~

Percent Increase and Decrease with Equations

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Learning Targets

I can solve percent increase and decrease problems by writing an equation to represent the situation and solving it.

Notes

We can use equations to express percent increase and percent decrease. For example, if y is 15% more than x,

we can represent this using any of these equations:

y = x + 0.15 x

y = (1 + 0.15) x

y = 1.15 x

So if someone makes an investment of x dollars, and its value increases by 15% to $1250, then we can write and solve the equation 1.15x=1250 to find the value of the initial investment.

Here is another example: if a is 7% less than b, we can represent this using any of these equations:

a = b − 0.07 b

a = (1 − 0.07) b

a = 0.93b

So if the amount of water in a tank decreased 7% from its starting value of b to its ending value of 348 gallons, then you can write 0.93 b = 348.

Often, an equation is the most efficient way to solve a problem involving percent increase or percent decrease.

Equivalent expressions with percent problemsCreate expressions with fractions and decimals to solve real world percent word problems.

Activities

8.2 Interest and Depreciation

Paying interest is paying a charge for borrowed money, usually based on a percentage. You can also collect interest when investing in a savings account.

Example: When borrowing from a bank or on a credit card, there is an interest charge in addition to the amount of the loan.

Depreciation is a decrease in the value or worth of something.

Example: Objects like cars, machinery, equipment, and currency lose value over time.

Money in a particular savings account increases by about 6% after a year. How much money will be in the account after one year if the initial amount is $100? $50? $200? $125? x dollars? If you get stuck, consider using diagrams or a table to organize your work.
The value of a new car decreases by about 15% in the first year. How much will a car be worth after one year if its initial value was $1,000? $5,000? $5,020? x dollars? If you get stuck, consider using diagrams or a table to organize your work.

8.3 Matching Equations

Match an equation to each of these situations. Be prepared to share your reasoning.

The water level in a reservoir is now 52 meters. If this was a 23% increase, what was the initial depth?
The snow is now 52 inches deep. If this was a 77% decrease, what was the initial depth?

0.23 x = 52 0.77 x = 52 1.23 x = 52 1.77 x = 52

Summary

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