Question

Hardy's sister is 4 years older than him. The sum of their ages is 32 years. Find Hardy's age.​

Answer 1

Let x = Hardy's age.

Then x + 4 = Hardy's sister's age.

x + x + 4 = 32

2x + 4 = 32

2x = 28

x = 14, so x + 4 = 18.

Hardy is now 14, and Hardy's sister is now 18.

Answer 2

Hardy is 14 years old.

Explanation:

To find Hardy's age, we can set up a system of equations based on the given information and then solve it.

Let "h" be Hardy's age (in years).

Let "s" be his sister's age (in years).

From the given information, we can form two equations.

Hardy's sister is 4 years older than him:

`s = h + 4`

The sum of their ages is 32:

`h + s = 32`

Therefore, the system of equations is:

`\begin{cases}s=h+4\\h+s=32\end{cases}`

Substitute the first equation into the second equation to eliminate the "s" term:

`h + (h + 4) = 32`

Combine like terms:

`2h + 4 = 32`

Subtract 4 from both sides of the equation:

`2h +4-4 = 32 - 4`

`2h = 28`

Divide by 2 to solve for h:

`(2h)/(2)=(28)/(2)`

`h = 14`

Therefore, Hardy is 14 years old.