SOLUTION: A vending machine takes only 20p and 50p coins and contains a total of twenty four coins all together. If the value of the coins is £6.90, find the number of coins of each value.

Let the number of 20p coins be x
Then the number of 50p coins, using
ONE PART = TOTAL MINUS OTHER PART,
is 24-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
20p          x        £0.20    £0.20x
50p        24-x       £0.50    £0.50(24-x)
-------------------------------------------
TOTALS      24        -----    £6.90

 The equation comes from the column on the right

  

0.20x + 0.50(24-x) = 6.90

Get rid of decimals by multiplying every term by 100

     20x + 50(24-x) = 690

   20x + 1200 - 50x = 690

        -30x + 1200 = 690

               -30x = -510

                  x = 17 = the number of 20p coins

The number of 50p is 24-x or 24-17 or 7 50p coins.

Checking:  17 20p coins is £3.40 and 7 50p is £3.50

And indeed £3.40+£3.50 = £6.90.

Edwin