Problem Solving With Percentages

8/2/2019 Problem Solving With Percentages

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Problem solving with percentagesClick on each percentage, then click on short cut to see some quick ways to work with this

percentage.Problem

Jos school is organising a trip, which costs 24.32 for each child. The school pays for 50%

of the cost, and the childrens parents pay for the other 50%. How much do the parents have

to pay?Answer

Half of 24.32 is 12.16. So the parents have to pay 12.16

Problem

25% of the cost of the trip (24.32) is for the childrens lunch. What will be the cost of each

childs lunch?

Answer

Half of 24.32 is 12.16. Half of 12.16 is 6.08. So the cost of each childs lunch is 6.08

ProblemIn an exam the pass mark is 75% out of a total of 60 marks. How many marks is the pass

mark?Halve to get 50% then halve again to get 25%. Then add the two together.

AnswerHalve 60 to get 50% = 30. Halve 30 to get 25% = 15. Add them together to get 75%: 30 + 15

= 45. So the pass mark is 45 marks.

Problem

In the same exam, Section 1 of the paper carries 10% of the 60 marks. How many marks are

there in Section 1?

Answer

Divide the total number of marks by 10. 60 10 = 6. So there are 6 marks in Section 1.

Problem

There are 320 children in the school where Jo works. 20% of them bring packed lunches.

How many children have packed lunches?

Answer

Divide 320 by 10 to get 10%.

320 10 = 32

Then double this to get 20%.32 doubled is 64.

So 64 children bring packed lunches.

Problem

40 people work at the school. At the end of term, 5% of them are leaving. How many peopleare leaving?Answer

Divide 40 by 10 to get 10%.

40 10 = 4

Then halve this to get 5%.

Half of 4 is 2.

So 2 people are leaving the school.


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If an amount increases by a percentage, you need to work out the percentage amount and addit on to the original amount.

Jo earns 14,500 a year. Her salary is going to increase by 5%. Jo wants to work out her new

salary after the increase.

Step 1: Work out the percentage amount - 5% of 14,500.

Click the buttons to see two ways of doing this calculation.Fraction method

5% = 1/20

1/20 of 14,500 = 14,500 20 = 725

5% of 14,500 is 725

Short cut method

5% is half of 10%

10% of 14,500 = 1450

Halve this to get 725

5% of 14,500 is 725Step 2: Add the percentage amount on to the original amount.

Watch the animation to see how to do this.Jos new salary = original salary + 5% increase

= 14,500 + 725

= 15,225

Jos new salary will be 15,225

If an amount decreases by a percentage, you need to work out the percentage amount and

subtract it from the original amount.

The cost of a box of poster paints is normally 26.20. In this special offer, there is a 25%

discount. Jo wants to work out the cost after the discount.

Step 1: Work out the percentage amount - 25% of 26.20.

Click the buttons to see two ways of doing this calculation.

Original cost: 26.20

Decrease: 25%Fraction method

25% =

of 26.20 = 26.20 4 = 6.55

25% of 26.20 is 6.55

Short cut method

25% is half of 50%

50% of 26.20 = 13.10

Halve this to get 6.55

25% of 26.20 is 6.55


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Step 2: Subtract the percentage amount from the original amount. Watch the animation to seehow to do this.

Original cost: 26.20Decrease: 25% = 6.55

Discounted price = original price 25% decrease

= 26.20 - 6.55

= 19.65The discounted price of the poster paints is 19.65

Calculating percentages with a calculator

Jos order comes to 192.40. She gets a 15% discount. How much will her discount be?

Method 1

Divide 192.40 by 100

1.924

Multiply by 15

28.86Jos discount is 28.86

Method 2Multiply 192.40 by 15

2886Divide by 100

28.86Jos discount is 28.86

Method 3

Divide 15 by 100 to change it to a decimal.

0.15

Multiply by 192.40

28.86

Jos discount is 28.86

Method 4

Use the % key

Enter 192.4 x 15%

28.86

Jos discount is 28.86

You can calculate percentage increase on a calculator. First calculate the increase and thenadd it to the original. Click on the arrows to see some ways of doing this.

A large tub of glue usually contains 500 ml. Special offer tubs contain 35% more. How muchglue will the special tub contain?

You can also calculate percentage decrease on a calculator. First calculate the decrease and

then subtract it from the original. Click on the arrows to see some ways of doing this.

Jo places another order for 234.99 and gets a 15% discount. How much will Jo pay after the

discount has been subtracted from the bill?


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Problem Solving With Percentages

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