Emily is twice as old as Matt. Three years ago, she was three times as old as he was. How old is Matt now?

We are given:

(a) E = 2M and

(b) E-3 = 3(M-3)

So:

2M - 3 = 3M - 9

solve for M.

Thank you Jim.

To solve this problem, we can use algebraic equations. Let's assume Matt's age is "x" years. According to the problem, Emily is twice as old as Matt, so her age would be 2x years.

Three years ago, Matt's age would have been (x - 3) years, and Emily's age would have been (2x - 3) years. The problem states that Emily was three times as old as Matt three years ago, so we can equate the two expressions:

2x - 3 = 3 * (x - 3)

Now let's solve the equation step by step:

2x - 3 = 3x - 9 [distribute 3 to (x - 3)]
2x - 3x = -9 + 3 [subtract 2x from both sides]
-x = -6 [combine like terms]
x = 6 [divide both sides by -1]

Therefore, Matt's age now is 6 years.