Theory question 104
Linear and Simultaneous Equations(a) Simplify 3/(m + 2n) − 2/(m − 3n)
(b) A number is made up of two digits. The sum of the digits is 11. If the digits are interchanged, the original number is increased by 9. Find the number.
Show the model answer
Model answer
(a) = [3(m − 3n) − 2(m + 2n)] / [(m + 2n)(m − 3n)]
= (3m − 9n − 2m − 4n)/[(m + 2n)(m − 3n)] = (m − 13n)/[(m + 2n)(m − 3n)]
(b) Let the number be 10t + u. Then t + u = 11
Interchanged: (10u + t) − (10t + u) = 9, so 9u − 9t = 9 and u − t = 1
Solving: u = 6, t = 5
The number is 56 (check: 65 − 56 = 9)
Explanation
A two-digit number with tens digit t and units digit u has value 10t + u.