Gabby and Lee collect beads and marbles. Lee has 50 less beads than marbles. Lee has 2 times the number of beads Gabby has, and Gabby has 40% more marbles than Lee. After Gabby gives Lee all of her beads and Lee gives Gabby 60% of his marbles, Lee has 13 more beads than marbles. Find the number of marbles Gabby has at first.
Gabby |
Lee |
Marbles |
Beads |
Marbles |
Beads |
2.8 u + 70 |
1 u |
2 u + 50 |
2 u |
+ 1.2 u + 30 |
- 1 u |
- 1.2 u - 30 |
+ 1 u |
4 u + 100 |
0 |
0.8 u + 20 |
3 u |
100%+ 40% = 140%
140% x 2 u
=
140100 x 2 u
= 2.8 u
140% x 50
=
140100 x 50
= 70
60% x 2 u
=
60100 x 2 u
= 1.2 u
60% x 50
=
60100 x 50
= 30
If another 13 marbles are given to Lee, he will have equal number of marbles and beads in the end.
3 u = 0.8 u + 20 + 13
3 u - 0.8 u = 33
2.2 u = 33
1 u = 33 ÷ 2.2 = 15
Number of marbles that Gabby has at first
= 2.8 u + 70
= 2.8 x 15 + 70
= 42 + 70
= 112
Answer(s): 112