## Finding the Whole given a Part and the Percentage

Practice Unlimited Questions

#### 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 Saved Actual 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

 1 8
of 40  =
 1 8
×  40

=  5

She painted 5 keyrings red.
30% of 40  =
 30 100
×  40

=  12

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

She painted 23 keyrings green.
Method 2 (changing fraction to percentage)

 1 8
of 100%  →
 1 8
×  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

He had 280 rock songs.
168  +  280  =  448

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.