1. Unit 6. Day 13.

2. Today’s Plan 1) Three interesting cases (successive percent change)
2) Review other problems

3. Example A: A store raises the price on a $100 dress 50%
Example A: A store raises the price on a $100 dress 50%. They then put the dress on sale for 50% off. What is the price of the dress?
−50%
+50%
$100
$150
$75

4. Take an additional 15% off
Example B: Two stores have a sale on a $300 camera. Which store has the better deal?
Store A:
50% discount
Store B: 40% discount
Take an additional 15% off 𝑥 𝑥
discount
40 100 𝑥
50 100
discount
15 100 = = =
300
original
300
180
original
15000 =
100 𝑥
100𝑥
12000 =
100 𝑥
100𝑥
2700
100 𝑥 =
100𝑥
100
100
100
100
100
100
150 = 𝑥
120 = 𝑥 27 = 𝑥
$ 3 0 0
$ 3 0 0
$ 1 8 0 −
$ 1 5 0 −
$ 1 2 0 −
$ 2 7
$ 1 5 0
$ 1 8 0
$ 1 5 3

5. Next day: 5% additional raise
Example C: Will Jordan and Frye make the same?
Mr. Jordan:
$20 per hour
15% raise
Mrs. Frye:
$20 per hour.
10% raise.
Next day: 5% additional raise 𝑥
15 100
raise
raise 𝑥 =
10 100 𝑥
5 100 20
original = =
original 20 22
15 20
300 =
100 𝑥
100𝑥
10 20
200
100 𝑥
100𝑥
5 22
110
100 𝑥
100𝑥 = =
100
100
100
100
100
100 3 = 𝑥 2 = 𝑥
1.1 = 𝑥
$ 20
$ 20
$ 22 +
$ 3 +
$ 2 −
$ 1.10
$ 2 3
$ 2 2
$ 23.10

6. Original Amount % Change New Amount
Example D: Milk increased from $2.40 per gallon to $3.60 Find the percent increase.
$2.40
$3.60 ?
Example E: A $3.75 bottle of orange juice is increased by 40%. What is the new price?
$3.75 ?
40%
Example F: A bottle of water cost $1.75 after a 25% increase. What was the original price?
$1.75
25% ?

7. Example D: Milk increased from $2. 40 per gallon to $3
Example D: Milk increased from $2.40 per gallon to $3.60 Find the percent increase.
2.40
increase
100 𝑥
1.20
increase =
original
2.40
original
2.4𝑥 =
120
2.4
2.4 𝑥 = = = 50
amount of increase
1.20
0. 5
% increase = =
original amount
50%

8. Example E: A $3. 75 bottle of orange juice is increased by 40%
Example E: A $3.75 bottle of orange juice is increased by 40%. What is the new price? 𝑥
increase
40 100
increase = =
140 𝑥
new
3.75
new
original
original
100
3.75
original
original
150 =
100 𝑥
100𝑥
100
100
525 =
100𝑥
1.5 = 𝑥
100
100
5.25 = 𝑥 $ + $ $

9. Example E: A $3. 75 bottle of orange juice is increased by 40%
Example E: A $3.75 bottle of orange juice is increased by 40%. What is the new price?
40%
40 % of $3.75 𝑜𝑓
3.75
0.40 ∙
3.75 $ − $ 3 2 ×
0. 4 1 . 5
1.40 ∙
3.75 =
5.25

10. Example F: A bottle of water cost $1. 75 after a 25% increase
Example F: A bottle of water cost $1.75 after a 25% increase. What was the original price?
increase
new
125 25
1.75
1.75
increase
new =
100 𝑥
original
100 𝑥
original
= 𝑥 5𝑥 = 7 5 5 𝑥 =
1.4

11. Example F: A bottle of water cost $1. 75 after a 25% increase
Example F: A bottle of water cost $1.75 after a 25% increase. What was the original price? 𝑥 ∙
1.25 =
1.75
1.25𝑥 =
1.75
1.25
1.25 . 𝑥 = .
5∙5∙7 =
5∙5∙5 =
1.40