Ronan and Kelsey each think of a number.2 less than Ronan's number is equal to 4 lots of Kelsey's number3 lots of Ronan's number added to Kelsey's number is 97Using the information above, write and solve two simultaneous equations to work out Ronan and Kelsey's numbers.

Solution

R o nan an d Ke l sey e a c h t hink o f a n u mb er .2 l ess t han R o na n^{'} s n u mb er i s e q u a l t o 4 l o t s o f Ke l se y^{'} s n u mb er 3 l o t s o f R o na n^{'} s n u mb er a dd e d t o Ke l se y^{'} s n u mb er i s 97 U s in g t h e in f or ma t i o n ab o v e, w r i t e an d so l v e tw o s im u lt an eo u s e q u a t i o n s t o w or k o u t R o nan an d Ke l se y^{'} s n u mb ers .

The number : \frac{- 24 + 570}{6} or - \frac{24 + 570}{6}

Solution steps

Represent the number with

x

A.T.Q.:

x - 2 = 4 x \cdot 3 x + x \cdot 97

Solve for

x, x - 2 = 4 x \cdot 3 x + x \cdot 97 : x = \frac{- 24 + 570}{6}, x = - \frac{24 + 570}{6}

The number : \frac{- 24 + 570}{6} or - \frac{24 + 570}{6}