Question

Find 2 whole numbers whose sum is 166 and difference is 32

Answer 1

a = 99 and b = 67

Step-by-step explanation:

Let the 2 numbers be a , b

Sum is 166

$a + b = 166 \\ \\ b = 166 − a \: \: \: \: ....(i)$

Difference is 32

$a - b = 32 \\ \\ a - ( 166 - a ) = 32 \\ \\ a - 166 + a = 32 \\ \\ 2a = 32 + 166 \\ \\ 2a = 198 \\ \\ a = \frac{198}{2} \\ \\ a = 99.$

put a = 99 in eq (i)

$b = 166 - a \\ \\ b = 166 - 99 \\ \\ b = 67.$

Answer 2

Answer: 99, 67

Step-by-Step Explanation:

Let the Larger Number be ‘a’
Let the Smaller Number be ‘b’

Sum = 166
Difference = 32

Therefore,
=> a + b = 166 (Eq. 1)
=> a - b = 32 (Eq. 2)

Adding Eq. 1 and 2, we get :-

2a = 198
a = 198/2
=> a = 99

Substitute value of ‘a’ in Eq. 2 :-

a - b = 32
(99) - b = 32
99 - b = 32
99 = 32 + b
99 - 32 = b
b = 99 - 32
=> b = 67

Therefore,
Larger Number: a => 99
Smaller Number: b => 67