Question

Find two numbers whose difference is 10 and their product is 96

Answer 1

Answer:

43 and 53

Step-by-step explanation:

trial and error

Answer 2

Answer:

The two numbers are 16 and 6 if the difference is 10 and their product is 96.

Explanation:

Let the numbers be  X and Y.

We know,

X - Y = 10 .......... (1)

XY = 96 ........... (2)

Let equation number one be marked as 1 and equation number two be marked as 2.

From equation number 1 we get,

X - Y = 10

∴ X = 10+ Y ......... (3).

We mark this new equation as 3.

Now, by the method of substitution, we substitute the value of X in equation number 2.

We get,

XY = 96

By method of substitution,

(10+Y)Y = 96

or, 10Y + $y^{2}$ = 96

or, $y^{2}$ + 10Y - 96 = 0

or, $y^{2}$ + 16y - 6y - 96 = 0

or, (y+16) (y-6) = 0

∴ Y = -16

or Y = 6

Y can not be negative, so Y = 6.

∴ XY = 96

X = 16.

Answer) The two numbers are 16 and 6.