Beth is two years older than Julio.Gerald is twice as old as Beth.Debra is twice as old as Gerald.The sum of their ages is 38.How old is Beth?

(1)2 (2)3 (3)5 (4)6 (5)8

B = J + 2

G = 2 B
D = 2 G
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so
J = B - 2
G = 2 B
D = 2 G = 4 B
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then
J + B + G + D = 38
( B-2 ) + B + 2 B + 4 B = 38

8 B = 40

B = 5

To find out how old Beth is, let's break down the problem step by step:

Let's assume Julio's age as "x."

According to the information given, Beth is two years older than Julio. So, Beth's age would be "x + 2."

Now, we know that Gerald is twice as old as Beth. Therefore, Gerald's age would be "2 * (x + 2)."

Similarly, Debra is twice as old as Gerald. So, Debra's age would be "2 * 2 * (x + 2)."

Now, we can sum up the ages of all four individuals to equal 38:

x + (x + 2) + 2 * (x + 2) + 2 * 2 * (x + 2) = 38

Now, let's solve this equation:

x + x + 2 + 2x + 4 + 4x + 8 = 38

Simplifying the equation:

8x + 14 = 38
8x = 24
x = 3

Therefore, Julio's age is 3.

Now we can find Beth's age by substituting x into her age:

Beth's age = x + 2 = 3 + 2 = 5

So, Beth is 5 years old.

Thus, the correct answer is (3) 5.