Daily Mail Mind Bender 8 Oct

[Magsiksnys]

In short my dad has 87 coins made up of 1p,2p and 10ps, equal number of 1p and 10ps. If total is £3.56, how many 2ps.

I got answer by trial and error. How would you do it algebraicll or ligically plese

 tia

[Fibonacci]

Let number of 1ps & 10ps = x (same number of each of these coins)
Let number of 2ps = y
Number of coins
 x + y + x = 87   or 2x+y =87 (1)
Value of coins in pence
x*1 + y*2 + x*10 = 356  
x+2y+10x = 356   or 11x + 2y = 356 (2)
You now have
(1)    2x + y =87  
(2)    11x + 2y = 356
Double (1) and subtract from (2)    
11x + 2y = 356  (2)
 4x + 2y  = 174  (1) doubled
7x + 0y   = 182   now divide by 7      
X = 26    
So 26 + y + 26 = 87   
Y+ 52 = 87
Y = 35
number of 1p coins = 26  
number of 2p coins =35
number of 10p coins = 26
check
value of coins = 26p + 70p +  260p = 356p = £3.56

 

[Magsiksnys]

Very nice ta