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 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.