Two numbers are in the ratio 3:2. if 5 subtracted to each the new ratio becomes 2:3 find the numbers.
> Solution

3 and 2

Step-by-step explanation:

The ratio of the 2 numbers = 3 : 2 = 3x : 2x ( x is a multiple )

When 5 is subtracted from both , that is

3x - 5 : 2x - 5 = 2 : 3

Expressing the ratio in fractional form

= ( cross- multiply )

3(3x - 5) = 2(2x - 5) ← distribute both sides

9x - 15 = 4x - 10 ( subtract 4x from both sides )

5x - 15 = - 10 ( add 15 to both sides )

5x = 5 ( divide both sides by 5 )

x = 1

Thus the 2 numbers are

3x = 3(1) = 3 and 2x = 2(1) = 2

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb