Question

Bettina is twice as old as Shirley. In three years, Bettina will be 13 years less than thrice as old as Shirley. How old is Shirley now

Answer 1

Shirley is currently 16 years old.

Step-by-step explanation:

To determine Shirley's age, let's denote her current age as S and Bettina's age as B. The given information states that Bettina is twice as old as Shirley, which can be expressed as B = 2S.

Now, considering the statement that in three years, Bettina will be 13 years less than thrice as old as Shirley, we can create an equation for their ages in three years:

`\[ B + 3 = 3(S + 3) - 13 \]`

Substitute
`\( B = 2S \)` into the equation:

`\[ 2S + 3 = 3(S + 3) - 13 \]`

Solve for S:

`\[ 2S + 3 = 3S + 9 - 13 \]`

Combine like terms:

`\[ 2S + 3 = 3S - 4 \]`

Subtract 2S from both sides:

`\[ 3 = S - 4 \]`

Add 4 to both sides:

`\[ S = 7 \]`

So, Shirley is currently 7 years old. However, remember that the initial question asks for Shirley's age now. To find that, substitute S back into the initial equation
`\( B = 2S \):`

`\[ B = 2(7) \]`

`\[ B = 14 \]`

Thus, Bettina is currently 14 years old. Therefore, Shirley is 7 years old now.