Olivia, Shannon and Yoko have equal number of pencils. Olivia packs all her pencils equally into 4 packets. Shannon packs all her pencils equally into 6 packets. Yoko packs all her pencils equally into 10 packets. 2 packets of Olivia's pencils, 4 packets of Shannon's pencils and 3 packets of Yoko's pencils add up to 176 pencils. How many pencils do they have altogether?
| |
Olivia |
Shannon |
Yoko |
| Number of packets |
4 |
6 |
10 |
| Number of pencils |
60 u |
60 u |
60 u |
| Number of pencils in each packet |
15 u |
10 u |
6 u |
All the pencils can be put into the packets without remainder.
All the children have equal numbers of pencils.
Make the number of pencils that each child has the same. LCM of 4, 6 and 10 = 60
Number of pencils that each child has = 60 u
Number of pencils in 1 packet of Olivia's pencils = 60 u ÷ 4 = 15 u
Number of pencils in 1 packet of Shannon's pencils = 60 u ÷ 6 = 10 u
Number of pencils in 1 packet of Yoko's pencils = 60 u ÷ 10 = 6 u
Number of pencils in 2 packets of Olivia's pencils, 4 packets of Shannon's pencils and 3 packets of Yoko's pencils
= (2 x 15 u) + (4 x 10 u) + (3 x 6 u)
= 30 u + 40 u + 18 u
= 88 u
88 u = 176
1 u = 176 ÷ 88 = 2
Total number of pencils that they have
= 3 x 60 u
= 180 u
= 180 x 2
= 360
Answer(s): 360
