Finding the Whole given a Part and the Percentage
Sherry bought a book shelf, a washing machine and a flower vase in a sale.
a) How much money did she save on the three items altogether?
b) What was the percentage discount on all the items together?
Solution:
Let's calculate the usual prices of the items.
Book shelf
Sherry paid 65% of the usual price for the book shelf.
65% → $78
1% → $78 ÷ 65
100% → $78 ÷ 65 × 100
= $120
The usual price of the book shelf is $120.
Let's calculate the usual prices of the items.
Book shelf
Sherry paid 65% of the usual price for the book shelf.
65% → $78
1% → $78 ÷ 65
100% → $78 ÷ 65 × 100
= $120
The usual price of the book shelf is $120.
Washing Machine
Discount = 30%
100% − 30% = 70%
Sherry paid 70% of the usual price for the washing machine.
70% → $140
1% → $140 ÷ 70
= $2
100% → $2 × 100
= $200
The usual price of the washing machine is $200.
Discount = 30%
100% − 30% = 70%
Sherry paid 70% of the usual price for the washing machine.
70% → $140
1% → $140 ÷ 70
= $2
100% → $2 × 100
= $200
The usual price of the washing machine is $200.
Flower Vase
Discount or off = 60%
100% − 60% = 40%
Sherry paid 40% of the usual price for the flower vase.
40% → $22
1% → $22 ÷ 40
100% → $22 ÷ 40 × 100
= $55
The usual price of the flower vase is $55.
Discount or off = 60%
100% − 60% = 40%
Sherry paid 40% of the usual price for the flower vase.
40% → $22
1% → $22 ÷ 40
100% → $22 ÷ 40 × 100
= $55
The usual price of the flower vase is $55.
a) The usual price of the three items together = $120 + $200 + $55
= $375
The sale price of the three items together = $78 + $140 + $22
= $240
Money saved on the three items together = $375 − $240
= $135
She saved $135 on the three items altogether.
= $375
The sale price of the three items together = $78 + $140 + $22
= $240
Money saved on the three items together = $375 − $240
= $135
She saved $135 on the three items altogether.
b) Percentage discount on the 3 items =
× 100%
=
× 100%
= 36%
The percentage discount on the 3 items together is 36%.
| Amount Saved |
| Actual Price |
=
| $135 |
| $375 |
= 36%
The percentage discount on the 3 items together is 36%.
Word Problem 1: In an auto show, 42.5% of the cars are used cars. Given that 714 cars are used cars, what is the total number of cars in the show?
42.5% → 714
1% → 714 ÷ 42.5
100% → 714 ÷ 42.5 × 100
= 1680
The total number of cars in the show is 1680.
1% → 714 ÷ 42.5
100% → 714 ÷ 42.5 × 100
= 1680
The total number of cars in the show is 1680.
Word Problem 2: Emily was 32 cm taller than Chloe. If Emily stood at 125% of Chloe's height, how tall was Emily?
25% → 32 cm
1% → 32 cm ÷ 25
100% → 32 cm ÷ 25 × 100
= 128 cm
Chloe was 128 cm tall.
128 cm + 32 cm = 160 cm
Emily was 160 cm tall.
1% → 32 cm ÷ 25
100% → 32 cm ÷ 25 × 100
= 128 cm
Chloe was 128 cm tall.
128 cm + 32 cm = 160 cm
Emily was 160 cm tall.
Word Problem 3: After a 15% service tax, Lisa's restaurant bill was $41.40. Find the amount of service tax she paid.
115% → $41.40
1% → $41.40 ÷ 115
100% → $41.40 ÷ 115 × 100
= $36
Lisa's bill before tax was $36.
$41.40 − $36 = $4.40
She paid $4.40 of service tax.
1% → $41.40 ÷ 115
100% → $41.40 ÷ 115 × 100
= $36
Lisa's bill before tax was $36.
$41.40 − $36 = $4.40
She paid $4.40 of service tax.
Word Problem 4: Emma painted
| 1 |
| 8 |
Method 1
of 40 =
× 40
= 5
She painted 5 keyrings red.
| 1 |
| 8 |
| 1 |
| 8 |
= 5
She painted 5 keyrings red.
30% of 40 =
× 40
= 12
She painted 12 keyrings blue.
| 30 |
| 100 |
= 12
She painted 12 keyrings blue.
40 − 5 − 12 = 23
She painted 23 keyrings green.
She painted 23 keyrings green.
Method 2 (changing fraction to percentage)
of 100% →
× 100%
= 12.5%
She painted 12.5% of the keyrings red.
12.5% + 30% = 42.5%
She painted 42.5% of the keyrings either red or blue.
100% − 42.5% = 57.5%
She painted 57.5% of the keyrings green.
| 1 |
| 8 |
| 1 |
| 8 |
= 12.5%
She painted 12.5% of the keyrings red.
12.5% + 30% = 42.5%
She painted 42.5% of the keyrings either red or blue.
100% − 42.5% = 57.5%
She painted 57.5% of the keyrings green.
100% → 40
1% → 40 ÷ 100
57.5% → 40 ÷ 100 × 57.5
= 23
She painted 23 keyrings green.
1% → 40 ÷ 100
57.5% → 40 ÷ 100 × 57.5
= 23
She painted 23 keyrings green.
Word Problem 5: Michael had a collection of hip-hop, rock and jazz music songs. He had 168 hip-hop songs. Hip-hop and rock made 70% of his collection. For every 3 hip-hop songs in his collection he had 5 rock songs. How many songs did he have in his collection?
Ratio of the number of hip-hop songs to the number of rock songs is 3 : 5.
3 units = 168
1 unit = 168 ÷ 3
= 56
5 units = 56 × 5
= 280
He had 280 rock songs.
3 units = 168
1 unit = 168 ÷ 3
= 56
5 units = 56 × 5
= 280
He had 280 rock songs.
168 + 280 = 448
He had 448 hip-hop and rock songs together.
He had 448 hip-hop and rock songs together.
70% → 448
1% → 448 ÷ 70
100% → 448 ÷ 70 × 100
= 640
He had 640 songs in his collection.
1% → 448 ÷ 70
100% → 448 ÷ 70 × 100
= 640
He had 640 songs in his collection.