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1. A public telephone has been vandalised and will take only 50 pence coins and 10 pence coins. A
woman puts £8.50 into the phone to make a long-distance call with twenty-five coins. Five 10
pence coins are returned when she finishes her call.
What combination of coins is retained by the machine?
A Twice as many 10s as 50s.
B One-and-a-half times as many 50s as 10s.
C The same number of 50s and 10s.
D Three times as many 50s as 10s.
E One-and-a-half times as many 10s as 50s.

2. Let x be the number of 50p and y the number of 10p coins initially inserted.
Then we can set up a simultaneous equation:
0.5x + 0.1y = 8.5, and x+y = 25 (as 25 coins are inserted)
Solving this quickly, x=15 and y=10.
Then we know that 5 10p are returned, so the machine has retained x 50p coins (15) and y-5 10p coins (5) which is the 3:1 ratio that option D provides

Updated: October 17, 2017
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