## 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

= $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%

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**

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)**

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.