SOLUTION: The sum of three numbers is 120. The second of the numbers is 8 less than the first, and the third number is 4 more than the first number. Thank you

Question 214358This question is from textbook Algebra Structure and Method Book 1
: The sum of three numbers is 120. The second of the numbers is 8 less than the first, and the third number is 4 more than the first number.
Thank you This question is from textbook Algebra Structure and Method Book 1

Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
Well first off you need to create the system of equations from the sentences you are given. Let the first number be x, the second number be y, and the third number be z. Then we know by the first sentence that x+y+z = 120. Now we know that the second number is 8 less than the first. In equations this would be y = x-8. We also know that the thirdn umber is 4 more than the first. This would be z = x+4.

So our system of equations is:

x+y+z = 120
y = x-8
z = x+4

Now we can substitute equations 2 and 3 into the first equation and solve for x.

x+y+z = 120
x+x-8+x+4 = 120
3x-4 = 120
3x = 124
x = 124/3

Now we can plug that value of x into our second and third equations to solve for y and z respectivly.

y = x-8 = 124/3 - 8 = 100/3
z = x+4 = 124/3 + 4 = 136/3

So our solution is (124/3, 100/3, 136/3)
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