Question

What least number must be added to each term of the ratio $$5 : 7$$ to make it $$8 : 9$$?

Answer 1

Let the number added be $$x$$. 

Then, $$\frac{5 + x}{7 + x} = \frac{8}{9}$$. 

Cross-multiply: $$9(5 + x) = 8(7 + x)$$

$$45 + 9x = 56 + 8x$$ 

Solve for $$x$$: $$9x - 8x = 56 - 45$$

$$x = 11$$ 

Therefore, the least number to be added is 11.