Groups, gaps and offers

In the last lesson, we undid a wrong calculation to find the number. Today, we will count the free item as part of each offer group. A beach stall offers one free shell badge for every 2 shell badges bought. Mei gets 18 shell badges, all from full offers. How many shell badges must Mei pay for? For each offer, Mei pays for 2 badges. Then she gets 1 more badge for free. Together, they make one offer group. The free badge is one of the badges Mei gets. 2 plus 1 is 3 badges in one group. Mei gets 18 badges altogether. The question asks only for the badges she pays for. So Mei's 18 badges come in groups of 3. 18 divided by 3 is 6 groups. In each group, she pays for only 2 badges. 6 times 2 is 12. So Mei pays for 12 shell badges.

A beach stall gives 1 free shell badge for every 3 shell badges bought. Kavin gets 20 shell badges, all from full offers. How many shell badges does Kavin pay for? Try it first. Pause if you like. For each offer, Kavin pays for 3 badges. Then he gets 1 more badge for free. Together, they make one offer group. The free badge is one of the badges Kavin gets. 3 plus 1 is 4 badges in one group. Kavin gets 20 badges altogether. The question asks only for the badges he pays for. So Kavin's 20 badges come in groups of 4. 20 divided by 4 is 5 groups. In each group, he pays for only 3 badges. 5 times 3 is 15. So Kavin pays for 15 shell badges.

A beach stall gives 1 free shell badge for every 2 shell badges bought. Each badge bought costs 3 dollars. Siti gets 15 shell badges, all from full offers. How much does Siti pay? Try it first. Pause if you like. For each offer, Siti pays for 2 badges. Then she gets 1 more badge for free. Together, they make one offer group. The free badge is one of the badges Siti gets. 2 plus 1 is 3 badges in one group. Siti gets 15 badges altogether. The question asks how much Siti pays. So Siti's 15 badges come in groups of 3. 15 divided by 3 is 5 groups. In each group, she pays for only 2 badges. 5 times 2 is 10. Each badge bought costs 3 dollars. Siti pays 3 dollars for each of the 10 badges she buys. 3 dollars times 10 is 30 dollars. So Siti pays 30 dollars. Count the free item in each offer group. Find the number of groups first, then the items paid for.