If Michelle is 7 years older than her sister Joan, who is 3 years younger than their brother Ryan, and the sum of their ages is 64, how old is Joan?

To determine Joan's age, we can set up the problem using algebra. Let's define the ages:

• Let Joan's age be represented by ( J ).

• Since Michelle is 7 years older than Joan, Michelle's age can be represented as ( J + 7 ).

• Ryan is the older sibling, and Joan is 3 years younger than Ryan, which means Ryan's age can be expressed as ( J + 3 ).

Now, we can formulate the equation based on the information that the sum of their ages is 64:

[

J + (J + 7) + (J + 3) = 64

]

Simplifying that equation gives:

[

J + J + 7 + J + 3 = 64

]

Combining like terms results in:

[

3J + 10 = 64

]

We subtract 10 from both sides of the equation:

[

3J = 54

]

Dividing both sides by 3 provides:

[

J = 18

]

Thus, Joan is 18 years old.

Choosing the correct answer relies on following the relationships outlined in the question. Joan's established age of 18 fits within