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

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Answer:

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.

User Molingran
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