Question

Five years ago, Mrs. Merlin was 8 times as old as her son, Josh. The sum of their present ages is 46. If Mr. Merlin is one year older than Mrs. Merlin, how old will Mr. Merlin be in two years from now?

Answer 1

Say that Mrs.Merlin's age was represented by x and Josh's age was represented by y. Therefore, as the sum of their ages is 46, x+y=46. Next, 5 years ago, Mrs. Merlin was 8 times as old as her son. To do this, we must first subtract 5 from each age to go to 5 years ago. Next, we must multiply Josh's age by 8 to get Mrs. Merlin's age, getting (y-5)*8=x-5

To make it a little neater, we can add 40 to both sides to get 8y=x+35. Subtracting x from both sides, 8y-x=35.

We then have two equations:

x+y=46

-x+8y=35.

If we add the two equations together using the elimination method, you'll notice that x is eliminated, so we have 9y=81. Dividing 9 from both sides to separate y, we get Josh's current age as 9. Next, since x+y=46, 9+x=46 and we can then subtract 9 from both sides to get Mrs. Merlin's age as 37. To get Mrs. Merlin's age in 2 years, we add 2 to her current age to get 39. Note that Mr. Merlin's age is not relevant because we need at least two pieces of information, and only one is given for him.

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