A coin bank contains some ten-cent and twenty-cent coins in the ratio of 2 : 7.
When 7 twenty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 6 : 7.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 7 = (3) |
(1) 10-cent |
(2) 20-cent |
Make p the same. (2) x 6 = (4) |
Before |
14 u |
2 u |
7 u |
42 u |
Change |
+ 98 |
+ 14 |
- 7 |
- 42 |
After |
42 p |
6 p |
7 p |
42 p |
Value of 7 twenty-cent coins
= 7 x 20
= 140¢
Number of ten-cent coins to exchange for
= 140 ÷ 10
= 14
2 u + 14 = 6 p --- (1)
7 u - 7 = 7 p --- (2)
Make p the same.
(1)
x 7 14 u + 98 = 42 p --- (3)
(2)
x 6 42 u - 42 = 42 p --- (4)
(4) = (3)
42 u - 42 = 14 u + 98
42 u - 14 u = 98 + 42
28 u = 140
1 u = 140 ÷ 28 = 5
Value of ten-cent coins
= 2 u x 10
= 2 x 5 x 10
= 100¢
Value of twenty-cent coins
= 7 u x 20
= 7 x 5 x 20
= 700¢
Total value of coins
= 100 + 700
= 800¢
100¢ = $1
Sum of money in the coin box
= 800¢
= $8
Answer(s): $8