Help I can't figure it out

Question

The sum of two numbers is 27. The larger number is 3 more than the smaller number. What are the two numbers? Use the substitution method or the elimination method.

Answer 1

SET UP YOUR EQUATIONS FROM THE TWO PIECES OF GIVEN INFORMATION

 

X = one number

Y = 2nd number

 

the sum is 27, so we write 

 

X + Y = 27

 

also we know, one number is 3 more than the 2nd number

 

X = 3 + Y    (we arbitrarily chose X to be larger, or more than Y)

 

substitute the value for X in the 2nd eqn, into the 1st eqn.

 

(3+Y) + Y = 27 

 3 + 2Y = 27           (now subtract 3 from each side to isolate Y)

       2Y = 24

 

so ===>  Y = 12   we then just plug this into either equation to get X (the other number)

 

    X = 3+Y = 3+12

    X = 15   <====

 

 so the two numbers are just   15,12   (or our X,Y found above)