# 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.

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.

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.

 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 savedActual price × 100% = \$135\$375 × 100% = 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.

### 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.

### 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.

### 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
 18 of 40 = 18 × 40 = 5
She painted 5 keyrings red.

 30% of 40 = 30100 × 40 = 12
She painted 12 keyrings blue.

40 − 5 − 12  =  23
She painted 23 keyrings green.

Method 2 (changing fraction to percentage)
 18 of 100% 18 × 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.

 100% 40 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