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Question 43 Tim's age was three-quarters of Mary's age 5 years ago. If Tim will be five-sixth of Mary's age in 3 years, what is the sum of their ages right now? Available Options A.28 B.35 C.38 D.41 E.none​

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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.

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