A total of 1541 shopping vouchers were given out at an event. Each man collected 2 vouchers, each woman collected 8 vouchers and each child collected 5 vouchers. Given that 3/7 of the people were men, 5/8 of the remainder were women and the rest were children, how many vouchers did the children collect?
men*2 women *8 children * 5
3/7x * 2 + 5/8 (4/7)* 8 x + 3/8 (4/7) x * 5 = 1541 x = number of people at event
(6/7 + 160/56 + 60/56 ) x = 1541
x = 322
children vouchers = 3/8 * 4/7 *5 * 322 = 345 vouchers
3/7 = 6/14 (fraction of total that are men)
1 - 3/7 = 4/7 = 8/14
(fraction of total that are women and children)
⅝ × 4/7 = 5/14
(fraction of the total that are women)
1 - 4/7 - 5/14 = 1 - 6/14 - 5/14 = 6/14
(fraction of the total that are children)
This tells you that ratio of men to women to children
= 6 : 5 : 3
Men → 2 vouchers each
Women → 8 vouchers each
Children → 5 vouchers each
Next, grouping concept.
6 men, 5 women, 3 children in 1 group.
Number of vouchers in 1 group
= 6 × 2 + 5 × 8 + 3 × 5
= 12 + 40 + 15
= 67
Number of groups
= 1541 ÷ 67
= 23
Number of children = 23 groups × 3 per group
= 69
Number of vouchers collected by them
= 69 × 5
= 345
