Vaidev has some ten-cent coins and fifty-cent coins which amount to more than $60 but less than $70. The number of ten-cent coins is
112 of all the coins he has. When he exchanges some fifty-cent coins for ten-cent coins, the ratio of the number of ten-cent coins to fifty-cent coins he now has become 9 : 1.
- What is the largest possible amount of money Vaidev has?
- What is the total value of fifty-cent coins that has been exchanged for ten-cent coins?
|
Ten-cent coins (1) |
Fifty-cent coins (2) |
Make b the same (2)x9 = (3) |
Before |
1 u |
11 u |
99 u |
Change |
+ 5 p |
- 1 p |
- 9 p |
After |
9 b |
1 b |
9 b
|
(a)
Total value of coins per set
= 1 x 10 + 11 x 50
= 10 + 550
= 560¢
$1 = 100¢
$70 = 7000¢
Number of sets of 560¢
= 7000 ÷ 560
= 12 r 280
Largest possible amount that Vaidev has
= 12 x 560
= 6720¢
= $67.20
(b)
Ten-cent coins : Fifty-cent coins = 1 : 11
1 u + 5 p =
9 b --- (1)
11 u - 1 p = 1 b --- (2)
Make b the same.
(2)
x9 = (3)
99 u - 9 p =
9 b --- (3)
(3) = (1)
99 u - 9 p = 1 u + 5 p
99 u - 1 u = 5 p + 9 p
98 u = 14 p
14 p = 98 u
1 p = 98 u ÷ 14 = 7 u
Since the number of sets of 560¢ is 12, 1 u is equal to 12.
Number of fifty-cent coins that have been exchanged for ten-cent coins
= 1 p
= 1 x 7 u
= 7 u
= 7 x 12
= 84
Total value of fifty-cent coins that have been exchanged for ten-cent coins
= 84 x 50
= 4200¢
= $42
Answer(s): (a) $67.20; (b) $42