IM 7.6.12 Lesson: Solving Problems about Percent Increase or Decrease

An item costs [math]x[/math] dollars and then a 20% discount is applied. Select [b]all[/b] the expressions that could represent the price of the item after the discount. 
Mai started a new exercise program. On the second day, she walked 5 minutes more than on the first day. On the third day, she increased her walking time from day 2 by 20% and walked for 42 minutes. Mai drew a diagram to show her progress.[br][br][img]data:image/png;base64,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[/img][br]Explain how the diagram represents the situation.
Noah said the equation [math]1.20\left(d+5\right)=42[/math] also represents the situation. Do you agree with Noah? Explain your reasoning.
Find the number of minutes Mai walked on the first day. Did you use the diagram, the equation, or another strategy? Explain or show your reasoning.
Mai has been walking indoors because of cold temperatures. On Day 4 at noon, Mai hears a report that the temperature is only 9 degrees Fahrenheit. She remembers the morning news reporting that the temperature had doubled since midnight and was expected to rise 15 degrees by noon. Mai is pretty sure she can draw a diagram to represent this situation but isn't sure if the equation is [math]9=15+2t[/math] or [math]2\left(t+15\right)=9[/math]. What would you tell Mai about the diagram and the equation and how they might be useful to find the temperature, [math]t[/math], at midnight?
A store is having a sale where all shoes are discounted by 20%. Diego has a coupon for $3 off of the regular price for one pair of shoes. The store first applies the coupon and then takes 20% off of the reduced price. If Diego pays $18.40 for a pair of shoes, what was their original price before the sale and without the coupon?
Before the sale, the store had 100 pairs of flip flops in stock. After selling some, they notice that [math]\frac{3}{5}[/math] of the flip flops they have left are blue. If the store has 39 pairs of blue flip flops, how many pairs of flip flops (any color) have they sold?
When the store had sold [math]\frac{2}{9}[/math] of the boots that were on display, they brought out another 34 pairs from the stock room. If that gave them 174 pairs of boots out, how many pairs were on display originally?
On the morning of the sale, the store donated 50 pairs of shoes to a homeless shelter. Then they sold 64% of their remaining inventory during the sale. If the store had 288 pairs after the donation and the sale, how many pairs of shoes did they have at the start?
A coffee shop offers a special: 33% extra free or 33% off the regular price. Which offer is a better deal? Explain your reasoning.

IM 7.6.12 Practice: Solving Problems about Percent Increase or Decrease

A backpack normally costs $25 but it is on sale for $21. What percentage is the discount?
Find each product.
[math]\frac{2}{5}\cdot\left(-10\right)[/math]
[math]-8\cdot\left(\frac{-3}{2}\right)[/math]
[math]\frac{10}{6}\cdot0.6[/math]
[math]\left(\frac{-100}{37}\right)\cdot\left(-0.37\right)[/math]
Select [b]all[/b] expressions that show [math]x[/math] increased by 35%.
Complete each sentence with the word discount, deposit, or withdrawal.
Clare took $20 out of her bank account. She made a _____.
Kiran used a coupon when he bought a pair of shoes. He got a _____.
Priya put $20 into her bank account. She made a _____.
Lin paid less than usual for a pack of gum because it was on sale. She got a _____.
The initial freshman class at a college is 10% smaller than last year’s class. But then during the first week of classes, 20 more students enroll. There are then 830 students in the freshman class.
Which equation matches this story?
Solve the equation you chose, and explain what the solution means in the situation.
A store reduces the price of a computer by $20. Then during a 10% off sale, a customer pays $830.
Which equation matches this story?
Solve the equation you chose, and explain what the solution means in the situation.
In the problems above, why does one equation have parentheses and the other doesn't?

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