A coin bank contains some ten-cent and twenty-cent coins in the ratio of 5 : 6.
When 10 twenty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 7 : 5.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 5 = (3) |
(1) 10-cent |
(2) 20-cent |
Make p the same. (2) x 7 = (4) |
Before |
25 u |
5 u |
6 u |
42 u |
Change |
+ 100 |
+ 20 |
- 10 |
- 70 |
After |
35 p |
7 p |
5 p |
35 p |
Value of 10 twenty-cent coins
= 10 x 20
= 200¢
Number of ten-cent coins to exchange for
= 200 ÷ 10
= 20
5 u + 20 = 7 p --- (1)
6 u - 10 = 5 p --- (2)
Make p the same.
(1)
x 5 25 u + 100 = 35 p --- (3)
(2)
x 7 42 u - 70 = 35 p --- (4)
(4) = (3)
42 u - 70 = 25 u + 100
42 u - 25 u = 100 + 70
17 u = 170
1 u = 170 ÷ 17 = 10
Value of ten-cent coins
= 5 u x 10
= 5 x 10 x 10
= 500¢
Value of twenty-cent coins
= 6 u x 20
= 6 x 10 x 20
= 1200¢
Total value of coins
= 500 + 1200
= 1700¢
100¢ = $1
Sum of money in the coin box
= 1700¢
= $17
Answer(s): $17