Question 572723:
Answer by mathsmiles(68)   (Show Source):
You can put this solution on YOUR website! Melinda's mother is four times as old as Melinda. In 16 years, her mother will twice her age. How old is melinda now?
Let's use X and Y to mean Melinda's age (X) and her mom's age (Y) today.
Melinda's mom is 4 times Melinda's age. So Y = 4X
In 16 years, Melinda will be X+16 and her mom will be Y+16. At that time Melinda's mom will be 2 times Melinda's ago. So if we double Melinda's age at that time, 2(X+16) that will equal Melinda's mom age at that time (Y+16).
Now, put these together. We need to solve for one variable - Melinda's age X.
Y=4X
2(X+16)=Y+16
Substituting for Y:
2(X+16) = (4X)+16
2X + 32 = 4X + 16. Subtract 2X from each side ...
32 = 2X +16. Subtract 16 from each side ...
16 = 2X. Divide both sides by 2 ...
8 = X.
So, going back to the original problem, Melissa is 8.
Now, let's check.
If Melinda is 8, then her mom is 4 time 8 = 32.
In 16 years, Melinda will be 8+16 = 24.
In 16 years, Melinda's mom will be 32+16 = 48.
Will her mom be 2 time Melinda's age then?
24 * 2 = 48. Correct!
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