Question

Two positive numbers have a difference of 4 and a product of 96. What are the numbers?

A. 12 and 8
B. 16 and 6
C. 16 and 12
D. 18 and 14

Answer 1

It'd be A.. You first would find which of them have a difference of 4. Which, is A, C, and D. Then, you'd multiply to see which of those three equal 96. 12*8=96

Answer 2

A. 12 and 8

Explanation:

Let x be the larger positive number and y be the smaller positive number.

Since, the difference between these number is 4,

⇒ x - y = 4,

⇒ x = 4 + y ------(1)

Also, the product of these number is 96,

⇒ xy = 96

From equation (1),

`(4+y)y = 96`

`4y+y^2=96`

`y^2+4y-96=0`

`y^2+12y-8y-96=0`

`y(y+12)-8(y+12)=0`

`(y-8)(y+12)=0`

By zero product property,

y-8=0 or y+12=0

y = 8 or y = - 12( not possible )

Again from equation (1),

x = 4 + 8 = 12,

Hence, the numbers are 12 and 8,

Option A is correct.