Cathy, Emily and Marion have equal number of beads. Cathy packs all her beads equally into 6 packets. Emily packs all her beads equally into 3 packets. Marion packs all her beads equally into 7 packets. 5 packets of Cathy's beads, 2 packets of Emily's beads and 6 packets of Marion's beads add up to 594 beads. How many beads do they have altogether?
| |
Cathy |
Emily |
Marion |
| Number of packets |
6 |
3 |
7 |
| Number of beads |
42 u |
42 u |
42 u |
| Number of beads in each packet |
7 u |
14 u |
6 u |
All the beads can be put into the packets without remainder.
All the children have equal numbers of beads.
Make the number of beads that each child has the same. LCM of 6, 3 and 7 = 42
Number of beads that each child has = 42 u
Number of beads in 1 packet of Cathy's beads = 42 u ÷ 6 = 7 u
Number of beads in 1 packet of Emily's beads = 42 u ÷ 3 = 14 u
Number of beads in 1 packet of Marion's beads = 42 u ÷ 7 = 6 u
Number of beads in 5 packets of Cathy's beads, 2 packets of Emily's beads and 6 packets of Marion's beads
= (5 x 7 u) + (2 x 14 u) + (6 x 6 u)
= 35 u + 28 u + 36 u
= 99 u
99 u = 594
1 u = 594 ÷ 99 = 6
Total number of beads that they have
= 3 x 42 u
= 126 u
= 126 x 6
= 756
Answer(s): 756
