Question 1168152: In three years, Sheena will be three times as old as her sister Melona, a year ago, Sheena was seven times as old as Melona. How old are they now?
Found 3 solutions by Theo, greenestamps, josgarithmetic:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let s = sheela's current age.
let m = melona's current age.
in 3 years, sheena will be 3 times as old as her sister melona.
equation for that is s + 3 = 3 * (m + 3)
a year ago, sheena was 7 times as old as melona.
equation for that is s - 1 = 7 * (m - 1)
solve for s in both equations to get:
s = 3 * (m + 3) - 3
s = 7 * (m - 1) + 1
simplify each equation to get:
s = 3 * m + 9 - 3
s = 7 * m - 7 + 1
combine like terms in each equation to get:
s = 3 * m + 6
s = 7 * m - 6
subtract the first equation from the second to get:
0 = 4 * m - 12
add 12 to both sides of the equation to get:
12 = 4 * m
solve for m to get:
m = 12 / 4 = 3
melona is currently 3 years old.
in the equation of s = 3 * m + 6, replace m with 3 to get:
s = 3 * 3 + 6 = 9 + 6 = 15
sheena is currently 15 years old.
sheena is 15 years old now and melona is 3 years old now.
3 years from now, sheena will be 18 and melona will be 6.
18 / 6 = 3 meaning sheena will be 3 times as old as melona in 3 years.
1 year ago, sheena was 14 and melona was 2.
14 / 2 = 7 meaning sheena was 7 times as old as melona 1 year ago.
the solution is confirmed to be good.
the solution is that sheena is 15 years old now and melona is 3 years old now.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The solution by the other tutor is fine; you should know how to set up and solve the problem using formal algebra in some way similar to his.
But you can get some very good practice with logical reasoning skills by solving the problem informally. Here is how this problem can be solved quickly without algebra.
(1) In 3 years, Sheena will be 3 times as old as Melona. That means her age 3 years from now will be a multiple of 3; and that means her current age is a multiple of 3: 3, 6, 9, 12, 15, 18, ...
(2) A year ago, Sheena was 7 times as old as Melona. That means her current age is 1 more than a multiple of 7: 1, 8, 15, 22, ...
The smallest age that satisfies both conditions is 15. See if that satisfies the conditions of the problem.
CHECK:
Sheena is 15; in 3 years she will be 15+3=18; so in 3 years Melona will be 18/3=6; so Melona is now 6-3=3.
Sheena is 15; a year ago she was 15-1=14; so a year ago Melona was 14/7=2; so now Melona is 2+1=3.
Everything checks....
ANSWER: Melona is 3 and Sheena is 15.
Answer by josgarithmetic(39617)  (Show Source):
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