Julie, Dana and Gillian have equal number of pencils. Julie packs all her pencils equally into 3 packets. Dana packs all her pencils equally into 7 packets. Gillian packs all her pencils equally into 6 packets. 2 packets of Julie's pencils, 3 packets of Dana's pencils and 5 packets of Gillian's pencils add up to 486 pencils. How many pencils do they have altogether?
| |
Julie |
Dana |
Gillian |
| Number of packets |
3 |
7 |
6 |
| Number of pencils |
42 u |
42 u |
42 u |
| Number of pencils in each packet |
14 u |
6 u |
7 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 3, 7 and 6 = 42
Number of pencils that each child has = 42 u
Number of pencils in 1 packet of Julie's pencils = 42 u ÷ 3 = 14 u
Number of pencils in 1 packet of Dana's pencils = 42 u ÷ 7 = 6 u
Number of pencils in 1 packet of Gillian's pencils = 42 u ÷ 6 = 7 u
Number of pencils in 2 packets of Julie's pencils, 3 packets of Dana's pencils and 5 packets of Gillian's pencils
= (2 x 14 u) + (3 x 6 u) + (5 x 7 u)
= 28 u + 18 u + 35 u
= 81 u
81 u = 486
1 u = 486 ÷ 81 = 6
Total number of pencils that they have
= 3 x 42 u
= 126 u
= 126 x 6
= 756
Answer(s): 756
