Equal at first

In the last lesson, one amount stayed the same while the other changed. Today, we will see how two changes make a difference. Mei and Kavin had equal numbers of shells at first. Mei received 8 shells from another box. Kavin gave 4 shells to a display. Mei then had 3 times as many shells as Kavin. How many shells did each have at first? They had equal numbers at first, so we draw two equal bars. At first, both bars end at the same place. Mei received 8 more shells, so her bar grows by 8. Kavin gave away 4 shells, so we mark off the end of his bar. The question asks how many each had at first. The 8 new shells and the 4 missing shells make the difference now. 8 plus 4 is 12. So now, the difference is 12 shells. Mei now has 3 units and Kavin has 1. 3 units minus 1 unit is 2 units. These 2 units are 12 shells. Kavin's shells now make 1 unit. 12 divided by 2 is 6. At first, Kavin also had the 4 he gave away. 6 plus 4 is 10. So each had 10 shells at first.

Siti and Bala had equal numbers of shells at first. Siti gave away 5 shells. Bala gave away 13 shells. Then Siti had 3 times as many shells as Bala. How many shells did each have at first? Try it first. Pause if you like. They had equal numbers at first, so we draw two equal bars. Siti gave away 5 shells, so we mark off the end of her bar. Bala gave away 13 shells, so we mark off the end of his bar. The question asks how many each had at first. Bala gave away more than Siti. The extra he gave away is the difference now. 13 minus 5 is 8. So now, the difference is 8 shells. Siti now has 3 units and Bala has 1. 3 units minus 1 unit is 2 units. These 2 units are 8 shells. 8 divided by 2 is 4. At first, Bala also had the 13 he gave away. 4 plus 13 is 17. So each had 17 shells at first.

Ravi and Wei Jie had equal numbers of shells at first. Ravi received 9 shells from another box. Wei Jie gave 3 shells to a display. Ravi then had 4 times as many shells as Wei Jie. How many shells did each have at first? Try it first. Pause if you like. They had equal numbers at first, so we draw two equal bars. Ravi received 9 more shells, so his bar grows by 9. Wei Jie gave away 3 shells, so we mark off the end of his bar. The question asks how many each had at first. Both changes make this difference. 9 plus 3 is 12. So now, the difference is 12 shells. Ravi now has 4 units and Wei Jie has 1. 4 units minus 1 unit is 3 units. These 3 units are 12 shells. 12 divided by 3 is 4. At first, Wei Jie also had the 3 he gave away. 4 plus 3 is 7. So each had 7 shells at first. When two amounts start equal, only the changes make the difference.