Question

Jess is 12 years less than half as old as Mac. The sum of their age is 87. How old is each person?

Answer 1

The age of each person is:

• Jess is 21 years old.
• Mac is 66 years old.

Explanation:

To solve this problem you must make two equations. First, we name Jess and Mac as variables:

j = Jess age.

m = Mac age.

Now we make the equations, the first equation has the information "Jess is 12 years less than half as old as Mac":

1.
`j=((m)/(2))-12`

The second equation has the information "The sum of their age is 87":

2.
`j+m=87`

Now, we replace the first equation in the second one:

• 
  `((m)/(2)-12) +m=87`

And we operate:

• 
  `(m-24)/(2) +m=87`
• 
  `(m-24+2m)/(2)=87`
• 
  `(3m-24)/(2)=87`

We clear the variable m:

• 
  `3m-24=87*2`
• 
  `3m=174+24`
• 
  `m=(198)/(2)`
• 
  `m=66`

How we know Mac's age is 66 years old, we can identify Jess' age with the second equation:

• 
  `j+m=87`

We replace the value of m:

• 
  `j+66=87`

And clear the variable j:

• 
  `j=87-66`
• 
  `j=21`

In the end, Jess's age is 21 years old.