SOLUTION: 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?

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?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 = 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 = (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 = (21+7)
21 = (28)
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