SOLUTION: one number is 8 more than another mumber, if 3 times the smaller is substracted from 5 times the larger number, the difference is 84 find the two mumbers

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Question 344816: one number is 8 more than another mumber, if 3 times the smaller is substracted from 5 times the larger number, the difference is 84 find the two mumbers
Found 2 solutions by checkley77, jsmallt9:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
x=y+8
5(y+8)-3x=84
5y+40-3(y+8)=84
5y+40-3y-24=84
2y=84-40+24
2y=68
y-68/2
y=34 ans.
x=34+8=42 ans.
Proof:
5(34+8)-3*42=84
5*42-126=84
210-126=84
84=84

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the larger number and let y = the smaller number.
Then from the problem we know
one number is 8 more than another number: x = y + 8
and
Five times the larger minus 3 times the smaller equals 84: 5x - 3y = 84
(NOTE: This second equation is correct. Another tutor's solution to this problem has a small error, using 3x instead of 3y. This is why that solution does not work out correctly.)

To solve this system of two equations of two variables, there are a variety of methods which can be used. Since the first equation is already "solved for x", the Substitution Method looks easiest. We will substitute the expression for x from the first equation into the second equation:
5(y+8) - 3y = 84
(Note the use of parentheses. It is an extremely good habit to use parentheses like this whenever you make a substitution. In this case it helps you know that we will be using the Distributive Property.)
Simplifying the left side:
5y + 40 - 3y = 84
2y + 40 = 84
Solving for y. Subtract 40 from each side:
2y = 44
Divide both sides by 2:
y = 22.

From above we can see that y is the smaller number. We can find x, the larger number, by using the equation x = y + 8, with y being 22:
x = (22) + 8 = 30

So the two numbers are 22 and 30.

These numbers actually check. One is 8 more than the other and 5 times the larger (5*30) minus 3 times the smaller (3*22) is 84:
5*30 - 3*22 = 84
150 - 66 = 84
84 = 84 Check!

(The other solution does not actually check. Its "proof" uses the same incorrect equation used to arrive at the incorrect answers being checked. 5*42 - 3*34 = 210 - 102 = 108 not 84.)