SOLUTION: ramon is 3 years older than sally. four times ramon's age ten years ago is 5 less than twice ramon's age now. how old are they now?

Question 177335: ramon is 3 years older than sally. four times ramon's age ten years ago is 5 less than twice ramon's age now. how old are they now?
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
let r = ramon's age.
let s = sally's age.
ramon is 3 years older than sally.
r = s + 3
ramon's age 10 years ago is:
r - 10
4 times ramon's age 10 years ago is:
4*(r-10)
twice ramon's age now is:
2*r
5 less than this is:
2*r - 5
4 times ramon's age 10 years ago is 5 less than twice ramon's age now.
4*(r-10) = 2*r - 5
since this second equation has one unknown, solve for r using this second equation.
4*(r-10) = 2*r - 5
remove parentheses:
4*r - 40 = 2*r - 5
subttract 2*r from both sides and add 40 to both sides to get:
4*r - 2*r = -5 + 40
combine like terms to get:
2*r = 35
r = 35/2 = 17.5
since r = s + 3, then:
s = 14.5
ramon is 17 and 1/2 years old now.
sally is 14 and 1/2 years old now.
to verify, substitute these values in the original equations.
use this relationship first:
four times ramon's age ten years ago is 5 less than twice ramon's age now.
ramon's age now is 17.5
ramons's age 10 years ago is 7.5
4 times 7.5 = 30
30 is 5 less than twice ramon's age now.
twice ramon's age now is 35
5 less than that is 30
30 = 30
looks good.
ramon is 3 years older than sally.
17.5 is 3 years older than 14.5
equations have been verified to be true.
your answer is:
ramon is 17.5 years old now.
sally is 14.5 years old now.

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