Sarah, Jane and Irene have equal number of buttons. Sarah packs all her buttons equally into 8 packets. Jane packs all her buttons equally into 10 packets. Irene packs all her buttons equally into 5 packets. 4 packets of Sarah's buttons, 5 packets of Jane's buttons and 3 packets of Irene's buttons add up to 576 buttons. How many buttons do they have altogether?
| |
Sarah |
Jane |
Irene |
| Number of packets |
8 |
10 |
5 |
| Number of buttons |
40 u |
40 u |
40 u |
| Number of buttons in each packet |
5 u |
4 u |
8 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 8, 10 and 5 = 40
Number of buttons that each child has = 40 u
Number of buttons in 1 packet of Sarah's buttons = 40 u ÷ 8 = 5 u
Number of buttons in 1 packet of Jane's buttons = 40 u ÷ 10 = 4 u
Number of buttons in 1 packet of Irene's buttons = 40 u ÷ 5 = 8 u
Number of buttons in 4 packets of Sarah's buttons, 5 packets of Jane's buttons and 3 packets of Irene's buttons
= (4 x 5 u) + (5 x 4 u) + (3 x 8 u)
= 20 u + 20 u + 24 u
= 64 u
64 u = 576
1 u = 576 ÷ 64 = 9
Total number of buttons that they have
= 3 x 40 u
= 120 u
= 120 x 9
= 1080
Answer(s): 1080
