Question
The difference between the two numbers is 23. Taking the larger number as x, find:
(i) the expression for a smaller number.
(ii) the smaller number, if the sum of these two numbers is 91.
✓
Answer
Difference of two numbers = 23
Let Larger number = x
(i) Then smaller number = x - 23
(ii) ∵ Sum of two numbers = 91
Then x + x - 23 = 91
⇒ 2x - 23 = 91
⇒ 2x = 91 + 23 = 114
$\Rightarrow x=\frac{114}{2}=57$
∴ Smaller number = x - 23 = 57 - 23 = 34
Let Larger number = x
(i) Then smaller number = x - 23
(ii) ∵ Sum of two numbers = 91
Then x + x - 23 = 91
⇒ 2x - 23 = 91
⇒ 2x = 91 + 23 = 114
$\Rightarrow x=\frac{114}{2}=57$
∴ Smaller number = x - 23 = 57 - 23 = 34
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