Vanessa, Gillian and Diana have equal number of pencils. Vanessa packs all her pencils equally into 10 packets. Gillian packs all her pencils equally into 4 packets. Diana packs all her pencils equally into 6 packets. 8 packets of Vanessa's pencils, 2 packets of Gillian's pencils and 4 packets of Diana's pencils add up to 590 pencils. How many pencils do they have altogether?
| |
Vanessa |
Gillian |
Diana |
| Number of packets |
10 |
4 |
6 |
| Number of pencils |
60 u |
60 u |
60 u |
| Number of pencils in each packet |
6 u |
15 u |
10 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 10, 4 and 6 = 60
Number of pencils that each child has = 60 u
Number of pencils in 1 packet of Vanessa's pencils = 60 u ÷ 10 = 6 u
Number of pencils in 1 packet of Gillian's pencils = 60 u ÷ 4 = 15 u
Number of pencils in 1 packet of Diana's pencils = 60 u ÷ 6 = 10 u
Number of pencils in 8 packets of Vanessa's pencils, 2 packets of Gillian's pencils and 4 packets of Diana's pencils
= (8 x 6 u) + (2 x 15 u) + (4 x 10 u)
= 48 u + 30 u + 40 u
= 118 u
118 u = 590
1 u = 590 ÷ 118 = 5
Total number of pencils that they have
= 3 x 60 u
= 180 u
= 180 x 5
= 900
Answer(s): 900
