A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 7.
When 19 fifty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 7 : 6.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 6 = (3) |
(1) 10-cent |
(2) 50-cent |
Make p the same. (2) x 7 = (4) |
Before |
30 u |
5 u |
7 u |
49 u |
Change |
+ 570 |
+ 95 |
- 19 |
- 133 |
After |
42 p |
7 p |
6 p |
42 p |
Value of 19 fifty-cent coins
= 19 x 50
= 950¢
Number of ten-cent coins to exchange for
= 950 ÷ 10
= 95
5 u + 95 = 7 p --- (1)
7 u - 19 = 6 p --- (2)
Make p the same.
(1)
x 6 30 u + 570 = 42 p --- (3)
(2)
x 7 49 u - 133 = 42 p --- (4)
(4) = (3)
49 u - 133 = 30 u + 570
49 u - 30 u = 570 + 133
19 u = 703
1 u = 703 ÷ 19 = 37
Value of ten-cent coins
= 5 u x 10
= 5 x 37 x 10
= 1850¢
Value of fifty-cent coins
= 7 u x 50
= 7 x 37 x 50
= 12950¢
Total value of coins
= 1850 + 12950
= 14800¢
100¢ = $1
Sum of money in the coin box
= 14800¢
= $148
Answer(s): $148