To solve this problem, you must name a variable, create expressions representing the parts of the problem, and then set up an equation.
Let Tim's age today be t. Since Tim's mom's age five years ago was 3 times Tim's current age, Tim's mom's current age is equal to 3t + 5.
Their ages are collectively 45, so Tim's age t and Tim's mom's age 3t + 5 must be equal to 45. Set up an equation and solve for the variable t.
45 = t + (3t + 5)
45 = t + 3t + 5
45 = 4t + 5
40 = 4t
10 = t
Tim is currently 10, and after plugging 10 for t into 3t + 5, we see that Tim's mom is 35.
Now let's check our work. Their combined ages are 45; 10 plus 35 is equal to 45, so that is correct. Further, addressing the "Five years ago, Tim's mom was three times Tim's age today" bit, we see that 10 - Tim's current age - times 3 is equal to 30, which would be Tim's mom's age 5 years ago.
Answer:
Today, Tim's mom is 35.