# Bar Model Solutions

**Year 6 Problems **

1. Three quarters of a number is 54. What is the number?

The bar model is a visual represent of the problem and the ratio table is a representation of multiplicative reasoning.

2. There are 36 packets of biscuits. One half are chocolate, a ninth are digestive and a third are wafer biscuits. The rest are ginger nuts. How many biscuits are ginger nuts?

Method 1

1/2 of 36 = 18

1/9 of 36 = 4

1/3 of 36 = 12

18 + 4 + 12 = 34

36 - 34 = 2

2 ginger nuts

Method 2

2 ginger nuts

3. There is 20% off in a sale. How much would a track suit cost, if the normal price was £44.50?

4. There is 20% off in a sale. The reduced price of the jeans is £36. What was the original price?

5. At a dance there are 4 girls to every 3 boys. There are 63 children altogether? How many girls are there?

6. Seven in every nine packets of crisps in a box are salt and vinegar. The rest are plain. There are 63 packets of salt and vinegar crisps. How many packets of plain crisps are there?

63 / 7 = 9

2 x 9 = 18

18 packets of plain crisps

**Key Stage 3 Problems **

1. Ralph posts 40 letters, some of which are first class, and some of which are second class. He posts four times as many second class letters as first. How many of each class of letter does he post? (This question appeared on a GCSE higher tier paper.)

8 first class and 32 second class

2. A computer game was reduced in a sale by 20% and it now costs £55 What was the original cost?

3. Sally had a bag of marbles. She gave one-third of them to Rebecca, and then one quarter of the remaining marbles to John. Sally then had 24 marbles left in the bag. How many marbles were in the bag to start with?

1/3 to Rebecca

1/4 of 2/3 = 1/6 to John

1 - 1/3 - 1/6 = 1/2 left

48 marbles to start

4. Sam bakes a variety of biscuits. 13 are peanut, 12 are raisin, the remaining 5 were oat. If you choose 1 biscuit at random, what is the probability that you will get an oat biscuit?

Probability of an oat biscuit = 5/30 = 1/6

5. Tom spent 30% of his pocket money and put away 45% into his savings. He was left with £2.50. How much pocket money did he receive?

6. Two numbers are in the ratio 4:5. They both sum to 135. Identify both numbers.

7. Two numbers are in the ratio 5 : 7. The difference between the numbers is 12. Work out the two numbers.

8. A herbal skin treatment uses yoghurt and honey in the ratio 5 : 3. How much honey is needed to mix with 130 g of yoghurt?