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

Mrs. Merlin's current age is 36, Josh's current age is 10, and Mr. Merlin's current age is 37. In two years from now, Mr. Merlin will be 39.

Step-by-step explanation:

To solve this problem, we can use algebraic equations. Let's denote Mrs. Merlin's current age as M and Josh's current age as J.

From the given information, we know that five years ago, Mrs. Merlin was 8 times as old as Josh:

M - 5 = 8(J - 5)

The sum of their present ages is 46:

M + J = 46

In addition, we are told that Mr. Merlin is one year older than Mrs. Merlin, so Mr. Merlin's current age can be denoted as M + 1.

Now we can solve the system of equations:

{ M - 5 = 8(J - 5)

{ M + J = 46

First, let's solve the second equation for M:

M = 46 - J

Substituting this expression for M into the first equation:

46 - J - 5 = 8(J - 5)

By simplifying and solving for J:

46 - J - 5 = 8J - 40

51 - J = 8J - 40

9J = 91

J = 10.111

Since age cannot be a decimal, we round it to the nearest whole number. Therefore, Josh's current age is 10.

To find Mrs. Merlin's current age, we can substitute the value of J into one of the equations:

M + 10 = 46

M = 36

Finally, Mr. Merlin's current age is M + 1:

M + 1 = 36 + 1 = 37.

In two years from now, Mr. Merlin will be 37 + 2 = 39 years old.

Answer 2

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.

Feel free to ask further questions!