Question

The smiths have two children. The sum of their ages is 23. The produce of their ages is 132. How old are the children?

Answer 1

For this case we propose a system of equations:

x: Let the variable representing the age of the first child of the Smiths

y: Let the variable representing the age of the second child of the Smiths

According to the data of the statement we have to:

`x + y = 23\\x * y = 132`

From the first equation we have to:

`x = 23-y`

We substitute in the second equation:

`(23-y) * y = 132\\23y-y ^ 2 = 132\\y ^ 2-23y + 132 = 0`

We find the solutions by factoring:

We look for two numbers that, when multiplied, result in 132 and when added, result in 23. These numbers are 11 and 12.

Thus, we have that the factorized equation is:

`(y-11) (y-12) = 0`

Thus, the solutions are:
`y_ {1} = 11\\y_ {2} = 12`

So, we can take any of the solutions:

With
`y = 11`

Then
`x = 23-11 = 12`

Therefore, the ages of the children are 11 and 12 respectively.

Answer:

The ages of the children are 11 and 12 respectively.