Neave 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 ¹₄ 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 11 : 1.

1. What is the largest possible amount of money Neave has?
2. 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)x11 = (3)
Before	1 u	3 u	33 u
Change	+ 5 p	- 1 p	- 11 p
After	11 b	1 b	11 b

(a)
Total value of coins per set
= 1 x 10 + 3 x 50
= 10 + 150
= 160¢ 

$1 = 100¢ 
$70 = 7000¢ 

Number of sets of 160¢ 
= 7000 ÷ 160
= 43 r 120

Largest possible amount that Neave has
= 43 x 160
= 6880¢ 
= $68.80

(b)
Ten-cent coins : Fifty-cent coins = 1 : 3

1 u + 5 p = 11 b --- (1)

3 u - 1 p = 1 b --- (2)

Make b the same.

(2)_x11 = (3)
33 u - 11 p = 11 b --- (3)

(3) = (1)
33 u - 11 p = 1 u + 5 p
33 u - 1 u = 5 p + 11 p
32 u = 16 p

16 p = 32 u

1 p = 32 u ÷ 16 = 2 u

Since the number of sets of 160¢ is 43, 1 u is equal to 43.

Number of fifty-cent coins that have been exchanged for ten-cent coins
= 1 p
= 1 x 2 u
= 2 u
= 2 x 43
= 86

Total value of fifty-cent coins that have been exchanged for ten-cent coins
= 86 x 50
= 4300¢
= $43

Answer(s): (a) $68.80; (b) $43