Respuesta :

yersanabria

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. [tex]j=(\frac{m}{2})-12[/tex]

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

2. [tex]j+m=87[/tex]

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

  • [tex](\frac{m}{2}-12) +m=87[/tex]

And we operate:

  • [tex]\frac{m-24}{2} +m=87[/tex]
  • [tex]\frac{m-24+2m}{2}=87[/tex]
  • [tex]\frac{3m-24}{2}=87[/tex]

We clear the variable m:

  • [tex]3m-24=87*2[/tex]
  • [tex]3m=174+24[/tex]
  • [tex]m=\frac{198}{2}[/tex]
  • [tex]m=66[/tex]

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

  • [tex]j+m=87[/tex]

We replace the value of m:

  • [tex]j+66=87[/tex]

And clear the variable j:

  • [tex]j=87-66[/tex]
  • [tex]j=21[/tex]

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

Otras preguntas