A coin bank contains some five-cent and fifty-cent coins in the ratio of 5 : 6.
When 16 fifty-cent coins are taken out and
exchanged with some five-cent coins of the same value,
the ratio became 8 : 7.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 7 = (3) |
(1) 5-cent |
(2) 50-cent |
Make p the same. (2) x 8 = (4) |
Before |
35 u |
5 u |
6 u |
48 u |
Change |
+ 1120 |
+ 160 |
- 16 |
- 128 |
After |
56 p |
8 p |
7 p |
56 p |
Value of 16 fifty-cent coins
= 16 x 50
= 800¢
Number of five-cent coins to exchange for
= 800 ÷ 5
= 160
5 u + 160 = 8 p --- (1)
6 u - 16 = 7 p --- (2)
Make p the same.
(1)
x 7 35 u + 1120 = 56 p --- (3)
(2)
x 8 48 u - 128 = 56 p --- (4)
(4) = (3)
48 u - 128 = 35 u + 1120
48 u - 35 u = 1120 + 128
13 u = 1248
1 u = 1248 ÷ 13 = 96
Value of five-cent coins
= 5 u x 5
= 5 x 96 x 5
= 2400¢
Value of fifty-cent coins
= 6 u x 50
= 6 x 96 x 50
= 28800¢
Total value of coins
= 2400 + 28800
= 31200¢
100¢ = $1
Sum of money in the coin box
= 31200¢
= $312
Answer(s): $312