Esther, Olivia and Shannon have equal number of buttons. Esther packs all her buttons equally into 4 packets. Olivia packs all her buttons equally into 3 packets. Shannon packs all her buttons equally into 9 packets. 3 packets of Esther's buttons, 2 packets of Olivia's buttons and 6 packets of Shannon's buttons add up to 750 buttons. How many buttons do they have altogether?
| |
Esther |
Olivia |
Shannon |
| Number of packets |
4 |
3 |
9 |
| Number of buttons |
36 u |
36 u |
36 u |
| Number of buttons in each packet |
9 u |
12 u |
4 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 4, 3 and 9 = 36
Number of buttons that each child has = 36 u
Number of buttons in 1 packet of Esther's buttons = 36 u ÷ 4 = 9 u
Number of buttons in 1 packet of Olivia's buttons = 36 u ÷ 3 = 12 u
Number of buttons in 1 packet of Shannon's buttons = 36 u ÷ 9 = 4 u
Number of buttons in 3 packets of Esther's buttons, 2 packets of Olivia's buttons and 6 packets of Shannon's buttons
= (3 x 9 u) + (2 x 12 u) + (6 x 4 u)
= 27 u + 24 u + 24 u
= 75 u
75 u = 750
1 u = 750 ÷ 75 = 10
Total number of buttons that they have
= 3 x 36 u
= 108 u
= 108 x 10
= 1080
Answer(s): 1080
