Justin had 100 more beads than Riordan. Justin gave 20% of his beads to Riordan. Riordan in return gave 50% of his beads to Justin. In the end, Justin had 346 more beads than Riordan. How many beads did Justin have at first?
| |
Justin |
Riordan |
Comparing Justin
and Peter at first |
100 more |
|
| Before |
5 u + 100 |
5 u |
| Change 1 |
- 1 u - 20 |
+ 1 u + 20 |
| After 1 |
4 u + 80 |
6 u + 20 |
| Change 2 |
+ 3 u + 10 |
- 3 u - 10 |
| After 2 |
7 u + 90 |
3 u + 10 |
20% =
20100 =
1520% x 100
=
20100 x 100
= 20
50% x 20
=
50100 x 20
= 10
50% x 6 u
=
50100 x 6 u
= 3 u
Justin had 346 more beads than Riordan in the end. If another 346 beads are given to Riordan, both will have the same number of beads.
7 u + 90 = 3 u + 10 + 346
7 u - 3 u = 10 + 346 - 90
7 u = 266
1 u = 266 ÷ 7 = 38
Number of Justin's beads at first
= 5 u + 100
= 5 x 38 + 100
= 190 + 100
= 290
Answer: 290
