10% of Charlie's savings was $54 more than 30% of Simon's savings. After Charlie spent
12 of his savings and Simon spent 40% of his savings, Charlie had $396 more than Simon. How much was Charlie's saving at first?
|
Simon |
Charlie |
Before |
10 u |
30 u + 540 |
Change |
- 4 u |
- 15 u - 270 |
After |
6 u |
15 u + 270 |
Comparing Simon and Charlie in the end |
|
396 more |
10% =
10100 =
110 30% =
30100 =
310 110 Charlie =
310 Simon + 54
Make the numerators the same. LCM of 1 and 3 is 3.
1x310x3 Charlie =
3x110x1 Simon + 54
330 Charlie =
310 Simon + 54
Simplify the fractions.
130 Charlie =
110 Simon + 18
Let
110 Simon be
1 u.
Simon's savings at first = 10 u
130 Charlie =
110 Simon + 18
Let
130 Charlie be
1 u + 18.
Charlie's savings at first
= 30 x (1 u + 18)
= 30 u + 540
Savings that Simon spent
= 40% x 10 u
=
40100 x 10 u
= 4 u
Savings that Charlie spent
=
12 x (30 u + 540)
= 15 u + 270
Charlie had $396 more than Simon in the end. If another $396 was given to Simon, the amount that each had in the end would be the same.
15 u + 270 = 6 u + 396
15 u - 6 u = 396 - 270
9 u = 126
1 u = 126 ÷ 9 = 14
Savings that Charlie had at first
= 30 u + 540
= 30 x 14 + 540
= 420 + 540
= $960
Answer(s): $960