MULTI STEP WORD PROBLEMS PERCENTAGE OF AMOUNTS

Problem 1 :

A supermarket has 1800 kg of root vegetables. 50% are potatoes and 25% are onions. What mass are the remaining root vegetables?

Solution:

= 1800 × (1 - 25% - 50%)

= 1800 × (1 - 0.25 - 0.5)

= 1800 × 0.25

= 450 kg

Problem 2 :

A school have a sponsored spell to raise money for their chosen charity, raising £764. 50% of the money is raised through dressing up. Of the remaining money, 25% is raised by selling cakes. The rest is raised by pupils paying to play games. How much is raised by playing games?

Solution:

50% of £764 is raised through dressing up.

50% × 764 = 382

764 - 382 = 382

25% of £382 is raised by selling cakes.

382 × 25% = 95.5

The rest is raised by pupils paying to play games.

382 - 95.5 = 286.5

£286.5 is raised by playing games.

Problem 3 :

A book is 340 pages long. 10% of the book is the introduction. Alex reads the introduction and 50% of the rest of the book in one week. How many pages are left to read?

Solution:

Total number of pages = 340

Introduction page = 10% = 0.1

= 340 (1 + 50% × (10% - 1) - 10%)

= 340 (1 + 0.5 × (0.1 - 1) - 0.1)

= 340 (1 + 0.5 × (-0.9) - 0.1)

= 340 (1 - 0.45 - 0.1)

= 340 × 0.45

= 153

153 pages are left to read.

Problem 4 :

A plasterer buys fifteen 25 kg bags of plaster. At the end of the week, only 10% of the plaster is left. How much plaster did they use?

Solution:

The plasterer bought 15 × 25 = 375 kg of plaster.

If only 10% is left, then they used 100 - 10 = 90% of the plaster.

So they used 375 × 90/100 = 337.5 kg of plaster.

Problem 5 :

A football team train for 18 hours every week. 25% of the time is spent on fitness and 10% on skills. The rest of the time is spent preparing for the next month. How long is spent on preparing for the next match?

Solution:

The football team spends 25% on fitness.

The football team also spend 10% on skills.

They train for 18 hours every week.

So, the percentage of time spent on preparing for next match is

= 100 - (25 + 10)%

= 100 - 35%

= 65%

So, time spent on preparing for next match is

= (65/100) × 18

= 11.7 hours

They spend 11.7 hours on preparing for their next match.

Problem 6 :

In a class of 30 children, 10% cycle to school. Another 10% come by bus. 25% of the remaining children come by car. The rest of the children walk. How many children walk to school?

Solution:

Number of cycling to school = 30 × 10% = 3

Number of going by bus = 30 × 10% = 3

Remaining students = 30 - 3 - 3 = 24

% going by car 25%

So, number of walking 24 × 75%

= 24 × (75/100)

= 18 children

Problem 7 :

The population of a town is 24 400. 25% of the people are children. 10% of the children are under the age of two. How many children under the age of two live in the town?

Solution:

Total number of population = 24400

percentage of children = 25%

percentage of children are under the age two = 10%

= 24400 × 25% × 10%

= 24400 × 0.25 × 0.1

= 610

Hence, 610 children under the age of two live in the town.

Problem 8 :

A school orders 80 packs of pencils. Each pack contains 12 pencils. 10% of the pencils are given out the day they arrive in school. How many pencils are given out on that first day?

Solution:

Order of pencils = 80 packs

Each pack = 12 pencils

= 80 × 12 × 10%

= 80 × 12 × 0.1

= 96 pencils

Problem 9 :

A bakery uses 48 kg of flour each day to bake bread. 2 kg of flour makes three loaves of bread. 25% of the loaves are wholemeal loaves. How many wholemeal loaves are baked each day?

Solution:

= 48/2 × 3 × 25%

= 72 × 0.25

= 18

Problem 10 :

A sunflower is measured at the beginning of June and is 40 cm tall. The sunflower grows by 25% each month for three months. What height is the sunflower to the nearest centimetre at the beginning of September?

Solution:

Beginning of July = (40 × 25% + 1)

= 40 × 0.25 + 1

= 40 × 1.25

= 50 cm

Beginning of  August = 50 × 1.25

= 62.5 cm

Beginning of September = 62.5 × 1.25

= 78.13 cm