A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 7.
When 14 fifty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 10 : 7.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 7 = (3) |
(1) 10-cent |
(2) 50-cent |
Make p the same. (2) x 10 = (4) |
Before |
35 u |
5 u |
7 u |
70 u |
Change |
+ 490 |
+ 70 |
- 14 |
- 140 |
After |
70 p |
10 p |
7 p |
70 p |
Value of 14 fifty-cent coins
= 14 x 50
= 700¢
Number of ten-cent coins to exchange for
= 700 ÷ 10
= 70
5 u + 70 = 10 p --- (1)
7 u - 14 = 7 p --- (2)
Make p the same.
(1)
x 7 35 u + 490 = 70 p --- (3)
(2)
x 10 70 u - 140 = 70 p --- (4)
(4) = (3)
70 u - 140 = 35 u + 490
70 u - 35 u = 490 + 140
35 u = 630
1 u = 630 ÷ 35 = 18
Value of ten-cent coins
= 5 u x 10
= 5 x 18 x 10
= 900¢
Value of fifty-cent coins
= 7 u x 50
= 7 x 18 x 50
= 6300¢
Total value of coins
= 900 + 6300
= 7200¢
100¢ = $1
Sum of money in the coin box
= 7200¢
= $72
Answer(s): $72