Sabrina, Joelle and Diana have equal number of buttons. Sabrina packs all her buttons equally into 6 packets. Joelle packs all her buttons equally into 5 packets. Diana packs all her buttons equally into 10 packets. 4 packets of Sabrina's buttons, 3 packets of Joelle's buttons and 5 packets of Diana's buttons add up to 530 buttons. How many buttons do they have altogether?
| |
Sabrina |
Joelle |
Diana |
| Number of packets |
6 |
5 |
10 |
| Number of buttons |
30 u |
30 u |
30 u |
| Number of buttons in each packet |
5 u |
6 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 6, 5 and 10 = 30
Number of buttons that each child has = 30 u
Number of buttons in 1 packet of Sabrina's buttons = 30 u ÷ 6 = 5 u
Number of buttons in 1 packet of Joelle's buttons = 30 u ÷ 5 = 6 u
Number of buttons in 1 packet of Diana's buttons = 30 u ÷ 10 = 3 u
Number of buttons in 4 packets of Sabrina's buttons, 3 packets of Joelle's buttons and 5 packets of Diana's buttons
= (4 x 5 u) + (3 x 6 u) + (5 x 3 u)
= 20 u + 18 u + 15 u
= 53 u
53 u = 530
1 u = 530 ÷ 53 = 10
Total number of buttons that they have
= 3 x 30 u
= 90 u
= 90 x 10
= 900
Answer(s): 900
