Question 696359
Steve is two thirds as old as Alex.
 In seven years, Steve will be three fourths as old as Alex.
 How old are they now?
:
let s = Steve's present age
Let a = Alex's age
:
Write an equation for each statement
:
"Steve is two thirds as old as Alex."
s = {{{2/3}}}a
get rid of the fraction, mult both side by 3
3s = 2a
3s - 2a = 0
:
" In seven years, Steve will be three fourths as old as Alex."
s + 7 = {{{3/4}}}(a+7)
mult both sides by 4
4(s+7) = 3(a + 7)
4s + 28 = 3a + 21
4s - 3a = 21 - 28
4s - 3a = -7
:
Use elimination here, mult the 1st equation by 3, the 2nd equation by 2
9s - 6s = 0
8s - 6a = -14
---------------subtraction eliminates a, find s
s = 14 yrs is Steve's age
then
3(14) - 2(a) = 0
42 - 2a = 0
-2a = -42
a = 21 yrs is Alex's age
;
:
Confirm this in the statement:
"In seven years, Steve will be three fourths as old as Alex."
14 + 7 = {{{3/4}}}(21+7)
21 = {{{3/4}}}(28)