Three quantities

In the last lesson, we set the difference aside so the bars made equal units. Today, we will draw three bars with the same unit, and build each bar from the bar it is compared with. Kavin, Mei and Siti have 46 shells altogether. Mei has 2 times as many shells as Kavin. Siti has 6 more shells than Mei. How many shells does Siti have? Mei has 2 times as many shells as Kavin, so Kavin's shells make 1 unit. So Mei's bar is 2 of these units. Siti has 6 more shells than Mei. So Siti's bar is as long as Mei's, and 6 more. The 6 more shells are only in Siti's bar. Together, the three of them have 46 shells. The question asks for Siti's shells. Set the 6 more shells aside, and only equal units are left. Now count the units in all three bars. 1 unit plus 2 units plus 2 units is 5 units. Without the 6, the 5 units are 46 minus 6. 46 minus 6 is 40. To find 1 unit, we share 40 equally among the 5 units. 40 divided by 5 is 8. So each unit is 8 shells. Siti has as many shells as Mei, and 6 more. Mei has 2 units. 2 times 8 is 16. 16 plus 6 is 22. So Siti has 22 shells.

Bala, Siti and Ravi have 47 shells altogether. Siti has 3 times as many shells as Bala. Ravi has 5 more shells than Siti. How many shells does Ravi have? Try it first. Pause if you like. Bala's shells make 1 unit. Siti's bar has 3 units. Ravi's bar is as long as Siti's, and 5 more. The 5 more are only in Ravi's bar. Together, they have 47 shells. Find Ravi's shells. Set the 5 aside, leaving equal units. Count all the units. 1 plus 3 plus 3 is 7 units. 47 minus 5 is 42. 42 divided by 7 is 6. Each unit is 6 shells. Ravi has Siti's shells and 5 more. 3 times 6 is 18. 18 plus 5 is 23. So Ravi has 23 shells.

Hui Min, Arjun and Dev have 73 shells altogether. Arjun has 4 times as many shells as Hui Min. Dev has 10 more shells than Arjun. How many shells does Arjun have? Try it first. Pause if you like. Hui Min's shells make 1 unit. Arjun's bar has 4 units. Dev's bar is as long as Arjun's, and 10 more. The 10 more are only in Dev's bar. Together, they have 73 shells. Find Arjun's shells. Set the 10 aside, leaving equal units. Count all the units. 1 plus 4 plus 4 is 9 units. 73 minus 10 is 63. 63 divided by 9 is 7. The question asks for Arjun. His bar has no extra part. 4 times 7 is 28. So Arjun has 28 shells. Draw every bar with the same unit. Set the extra aside, count all the units, then find one unit.