10% of Rael's savings was $60 more than 30% of Ivan's savings. After Rael spent
310 of his savings and Ivan spent 40% of his savings, Rael had $585 more than Ivan. How much was Rael's saving at first?
|
Ivan |
Rael |
Before |
10 u |
30 u + 600 |
Change |
- 4 u |
- 9 u - 180 |
After |
6 u |
21 u + 420 |
Comparing Ivan and Rael in the end |
|
585 more |
10% =
10100 =
110 30% =
30100 =
310 110 Rael =
310 Ivan + 60
Make the numerators the same. LCM of 1 and 3 is 3.
1x310x3 Rael =
3x110x1 Ivan + 60
330 Rael =
310 Ivan + 60
Simplify the fractions.
130 Rael =
110 Ivan + 20
Let
110 Ivan be
1 u.
Ivan's savings at first = 10 u
130 Rael =
110 Ivan + 20
Let
130 Rael be
1 u + 20.
Rael's savings at first
= 30 x (1 u + 20)
= 30 u + 600
Savings that Ivan spent
= 40% x 10 u
=
40100 x 10 u
= 4 u
Savings that Rael spent
=
310 x (30 u + 600)
= 9 u + 180
Rael had $585 more than Ivan in the end. If another $585 was given to Ivan, the amount that each had in the end would be the same.
21 u + 420 = 6 u + 585
21 u - 6 u = 585 - 420
15 u = 165
1 u = 165 ÷ 15 = 11
Savings that Rael had at first
= 30 u + 600
= 30 x 11 + 600
= 330 + 600
= $930
Answer(s): $930