In this lesson, students represent situations involving percent increase and percent decrease using equations. They write equations like \(y = 1.06x\) to represent growth of a bank account, and use the equation to answer questions about different starting amounts. They write equations like \(t - 0.25t = 12\) or \(0.75t=12\) to represent the initial price \(t\) of a T-shirt that was \$12 after a 25% discount. The focus of this unit is writing equations and understanding their connection to the context. In a later unit on solving equations the focus will be more on using equations to solve problems about percent increase and percent decrease.
When students repeatedly apply a percent increase to a quantity and see that this operation be expressed generally by an equation, they engage in MP8.
- Explain (orally and in writing) how to calculate the original amount given the new amount and a percentage of increase or decrease.
- Generate algebraic expressions that represent a situation involving percent increase or decrease, and justify (orally) the reasoning.
Let’s use equations to represent increases and decreases.
- I can solve percent increase and decrease problems by writing an equation to represent the situation and solving it.
A percentage decrease tells how much a quantity went down, expressed as a percentage of the starting amount.
For example, a store had 64 hats in stock on Friday. They had 48 hats left on Saturday. The amount went down by 16.
This was a 25% decrease, because 16 is 25% of 64.
A percentage increase tell how much a quantity went up, expressed as a percentage of the starting amount.
For example, Elena had \$50 in the bank on Monday. She had \$56 on Tuesday. The amount went up by \$6.
This was a 12% increase, because 6 is 12% of 50.