the total age of a woman and her son is 51 years. three years ago the woman was eight times as old as her son. how old is her son now?

Answer 1

Let "w" be the age of the woman and "s" be the age of her son.Since "the total age of a woman and her son is 51 years", we can say w + s = 51.

When we say "three years ago . . .", we can say that three years ago the woman's age was w - 3 an we can say her son's age was s - 3. Since "three years ago the woman was eight times as old as her son" then (w - 3) = 8(s - 3)

Simplifying this 2nd equation we get:

(w - 3) = 8(s - 3)

w - 3 = 8s - 24

w - 8s = -21

Those are our two equations we can solve to find the ages.

w + s = 51

w - 8s = -21

To solve by substitution, we can solve the second equation for w to get w = 8s - 21 then plug "8s - 21" into the first equation wherever we see "w"

To solve be elimination, we can multiply the 2nd equation by -1 and add the equations:

w + s = 51

-w + 8s = 21

9s = 72

s = 8

w = 43

(three years ago, the woman would have been 40 and the son would have been 5)