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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