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

Answer:

The age of each person is:

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

Step-by-step 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. $j=(\frac{m}{2})-12$

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:

• $(\frac{m}{2}-12) +m=87$

And we operate:

• $\frac{m-24}{2} +m=87$
• $\frac{m-24+2m}{2}=87$
• $\frac{3m-24}{2}=87$

We clear the variable m:

• $3m-24=87*2$
• $3m=174+24$
• $m=\frac{198}{2}$
• $m=66$

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.