Jean, Abi and Nora have equal number of buttons. Jean packs all her buttons equally into 5 packets. Abi packs all her buttons equally into 6 packets. Nora packs all her buttons equally into 10 packets. 2 packets of Jean's buttons, 5 packets of Abi's buttons and 3 packets of Nora's buttons add up to 230 buttons. How many buttons do they have altogether?
| |
Jean |
Abi |
Nora |
| Number of packets |
5 |
6 |
10 |
| Number of buttons |
30 u |
30 u |
30 u |
| Number of buttons in each packet |
6 u |
5 u |
3 u |
All the buttons can be put into the packets without remainder.
All the children have equal numbers of buttons.
Make the number of buttons that each child has the same. LCM of 5, 6 and 10 = 30
Number of buttons that each child has = 30 u
Number of buttons in 1 packet of Jean's buttons = 30 u ÷ 5 = 6 u
Number of buttons in 1 packet of Abi's buttons = 30 u ÷ 6 = 5 u
Number of buttons in 1 packet of Nora's buttons = 30 u ÷ 10 = 3 u
Number of buttons in 2 packets of Jean's buttons, 5 packets of Abi's buttons and 3 packets of Nora's buttons
= (2 x 6 u) + (5 x 5 u) + (3 x 3 u)
= 12 u + 25 u + 9 u
= 46 u
46 u = 230
1 u = 230 ÷ 46 = 5
Total number of buttons that they have
= 3 x 30 u
= 90 u
= 90 x 5
= 450
Answer(s): 450
