SOLUTION: Hi, I know I could get one question like this if someone could explain it to me - Three times the smaller of 2 numbers increased by 5 times the larger is 229. Four times the smalle

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Question 76284: Hi, I know I could get one question like this if someone could explain it to me - Three times the smaller of 2 numbers increased by 5 times the larger is 229. Four times the smaller decreased by 25 equals 3 times the larger. Find the numbers.
I started out with - x=bigger number, and y=smaller number
3y+5x=229 (first equation)
4y-25=3x (second equation)
How do you go on?
Answer by wodkit02(9) About Me  (Show Source):
You can put this solution on YOUR website!
Once you have 2 simultaneous equations, you can solve for a variable in one equation by using a modified version of the other.
For this particular question, your equations are correct. So we have
3y+5x=229
4y-25=3x
I'm going to start by putting the 2nd equation in terms of x, so when I solve for x I get:
4y-25=3x
%284y-25%29%2F3=x (I divided each side by 3)
Now I can plug in that x value into the 1st equation, so I can solve for y.
3y+5x=229
3y+5*%28%284y-25%29%29%2F3=229....distribute the 5 to everything in the parenthesis to get
3y+%2820y-125%29%2F3=229....now convert each term on the left side into like fractions of denominator 3 to get
%289y%2F3%29+%2820y-125%29%2F3=229....now multiply each side by 3 to get rid of the fraction to get
9y+20y-125=687...add like terms to get
29y-125=687...add 125 to each side to get
29y=812...finally, we can divide to get
y=28
Back to the 2nd equation, we can now plug in a number for y, and then solve for x:
4y-25=3x
4(28)-25=3x
112-25=3x
87=3x
29=x
So the numbers are 28 and 29.