Unit 4 Fractions and percentages 4 Problem-solving Objective • Use bar models to help you solve problems. Example 14 Sophie spends 40% of her birthday money on a necklace, and _12 of the remainder on earrings. She is left with £16.50. How much birthday money did Sophie receive? Draw a rectangular bar to represent all the birthday money. necklace Split the bar into 10% sections. Label 40% for the necklace. 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% necklace earrings Label _ 12 of the remainder for earrings. necklace earrings £16.50 Label the £16.50 she has left. 1 section = £16.50 ÷ 3 = £5.50 3 sections = £16.50. Work out 1 section. Total birthday money = £5.50 × 10 = £55 The bar represents all the birthday money. Check: Sophie spends Check your answer. 40% of £55 on a necklace: 40% of £55 = 4 x 10% of £55 = 4 x £5.50 = £22 __ 1 of £33 = £16.50 1 of the remainder on earrings: remainder = £55 − £22 = £33; __ 2 2 She has £16.50 left. Total = £22 + £16.50 + £16.50 = £55 3 1 At a pantomime, 60% of the audience are children. _ 14 of the remaining audience are men. The rest of the audience are women. There are 45 women in the audience. How many people are at the pantomime? 2 A small business has 16 employees. They are working on two different projects, project A and project B. 4 employees are working only on project A. 6 employees are working on both project A and project B. 2 employees are not working on either project. a How many employees are working on project B only? b How many employees, in total, are working on project B? Q1 hint Draw a bar to represent all the audience. Split the bar into 10% sections. Work out what 1 section represents. Then work out the total number of people in the audience. Q2a hint Draw a bar to represent all the employees working for the business. How many sections should you split the bar into? Q2b hint Total number of employees working on project B = employees working on both project A and project B + employees working on project B only. 111