Question

one number is greater than thrice the other number by 2.if 4 times the smaller number exceeds the greater by 5,find the number

Answer 1

Let the smaller number be α
Let the greater number be β
∴ β=3α+2 and,                                                   ... ... ... (i)
   4α-5=β                                                            ... ... ... (ii)
∴ 4α-5=3α+2                                                   [Inserting the value of β in (ii)] 
∴ 4α-3α=2+5
∴ α=7
Now, putting the given equation (ii);
4α-5=β
∴ 4(7)-5=β
∴ β=28-5
∴ β=23
∴ The answer to this question is that the value of α and β are 7 and 23 respectively.