# 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.

The usual price of the book shelf is $120.

65% $78 1% $78 ÷ 65 100% $78 ÷ 65 × 100 = $120

Washing machine

Sherry paid 70% of the usual price for the washing machine.

Discount = 30% 100% − 30% = 70%

The usual price of the washing machine is $200.

70% $140 1% $140 ÷ 70 = $2 100% $2 × 100 = $200

Flower vase

Sherry paid 40% of the usual price for the flower vase.

Discount or off = 60% 100% − 60% = 40%

The usual price of the flower vase is $55.

40% $22 1% $22 ÷ 40 100% $22 ÷ 40 × 100 = $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.

b) Percentage discount on the 3 items = Amount saved

Actual price× 100% = $135

$375× 100% = 36%

The percentage discount on the 3 items together is 36%.

*Word Problem 1*

*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.

*Word Problem 2*

*Word Problem 2*

Emily was 32 cm taller than Chloe. If Emily stood at 125% of Chloe's height, how tall was Emily?

Chloe was 128 cm tall.

25% 32 cm 1% 32 cm ÷ 25 100% 32 cm ÷ 25 × 100 = 128 cm

128 cm + 32 cm = 160 cm

Emily was 160 cm tall.

*Word Problem 3*

*Word Problem 3*

After a 15% service tax, Lisa's restaurant bill was $41.40. Find the amount of service tax she paid.

Lisa's bill before tax was $36.

115% $41.40 1% $41.40 ÷ 115 100% $41.40 ÷ 115 × 100 = $36

$41.40 − $36 = $4.40

She paid $4.40 of service tax.

*Word Problem 4*

*Word Problem 4*

Emma painted 1/8 of her 40 keyrings red, 30% of them blue and the rest of them green. How many keyrings did she paint green?

Method 1

She painted 5 keyrings red.

1

8of 40 = 1

8× 40 = 5

She painted 12 keyrings blue.

30% of 40 = 30

100× 40 = 12

40 − 5 − 12 = 23

She painted 23 keyrings green.

(changing fraction to percentage)Method 2

She painted 12.5% of the keyrings red.

1

8of 100% 1

8× 100% = 12.5%

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.

She painted 23 keyrings green.

100% 40 1% 40 ÷ 100 57.5% 40 ÷ 100 × 57.5 = 23

*Word Problem 5*

*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.

He had 280 rock songs.

3 units = 168 1 unit = 168 ÷ 3 = 56 5 units = 56 × 5 = 280

168 + 280 = 448

He had 448 hip-hop and rock songs together.

He had 640 songs in his collection.

70% 448 1% 448 ÷ 70 100% 448 ÷ 70 × 100 = 640