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Age 11 to 14 Challenge Level:

The problem was essentially a simple one using addition and algebra.

The solutions are:

(i)

(ii)

This gave a = 19 + 33 = 52

(iii)

All the solutions to this came from the relationship x + y = 2.
The value of b was 10.

N.B. Allowing negative integers here, there are infinitely many possible values for x and y, but only one possible value of b .

(iv)

The relationship for x and y is given as:
x + 3 y = 27.

By choosing whole number values for y , this relationship will always give whole number values for x . Again here, allowing for negative integers , there are infinitely many possible values for x and y .