In a film, actor charles coburn plays an elderly "uncle" character criticized for marrying a woman when he is 3 times her age. he wittily replies, "ah, but in 30 years time i shall only be twice her age." using algebra as opposed to "trial & error", how old is the "uncle" and the woman?

each answer must be explained in detail using the correct vocabulary to receive full credit.

Age of uncle = 90 years

Age of woman = 30 years

Step-by-step explanation:

Let the age of uncle be x years

And age of woman be y years

Now, uncle is three times her age ⇒ x = 3y (1)

Also, in 30 years uncle is twice her age ⇒ x + 30 = 2(y + 30) (2)

Now, substituting x = 3y from equation (1) in equation (2)

⇒ 3y + 30 = 2y + 60

⇒ y = 30

So, x = 90

Hence, Age of uncle = 90 years

Age of woman = 30 years

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3