Answer:
E. none
Explanation:
Let's use algebra to solve the problem:
Let's start by defining some variables. We'll use T for Tim's current age, and M for Mary's current age.
According to the first sentence of the problem, "Tim's age was three-quarters of Mary's age 5 years ago." In other words, we can write:
T - 5 = (3/4)(M - 5)
We can simplify and rearrange this equation to get:
4T - 20 = 3M - 15
4T = 3M + 5
According to the second sentence of the problem, "Tim will be five-sixth of Mary's age in 3 years." In other words, we can write:
T + 3 = (5/6)(M + 3)
Again, we can simplify and rearrange this equation to get:
6T + 18 = 5M + 15
6T = 5M - 3
Now we have two equations with two variables (4T = 3M + 5 and 6T = 5M - 3). We can use these equations to solve for T and M.
Multiplying the first equation by 2, we get:
8T = 6M + 10
Multiplying the second equation by 3, we get:
18T = 15M - 9
We can now solve for M by subtracting the first equation from the second:
10T = 21
T = 2.1
Substituting this value of T into one of the equations (e.g. 4T = 3M + 5), we can solve for M:
4(2.1) = 3M + 5
M = 8.3
Therefore, Tim's current age is 2.1 years and Mary's current age is 8.3 years.
The sum of their ages right now is T + M = 2.1 + 8.3 = 10.4 years.
So the sum of Tim and Mary's ages right now is 10.4 years.