SOLUTION: one number is four greater than another number when three times the smaller number is added to twice the larger number the result is 43. Could you please give me the method to w

Question 264508: one number is four greater than another number when three times the smaller number is added to twice the larger number the result is 43.
Could you please give me the method to work it out i know the answer is 7 i just don't know how to get there.
Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
Just break down what you are given, like this:

One number (make it "x")
is (=)
four greater (4 +)
than another number (make it "y"):
EQUATION: x = 4 + y

when three times the smaller number (the smaller number is y, so 3 times y: 3y) is added (3y +)to
twice the larger number (2 times the larger: 2x)
the result is (=) 43.
EQUATION: 3y + 2x = 43

Now you have TWO equations:
x = 4 + y
3y + 2x = 43

Solve this system. Do you see that x = 4 + y? SO instead of "X" in the 2nd equation, put in 4 + y, like this:

3y + 2x = 43 (original equation)
3y + 2(4 + y) = 43 (Plugged in 4 + y for the "X" variable)
3y + 8 + 2y = 43 (distributed 2 to the 4 and 2 to the y)
5y + 8 = 43 (combined like terms)
5y = 35 (subtracted 8 from both sides to isolate the y)
y = 7 (divided both sides by 5 to further isolate the y)

Now we know y = 7.

Plug in 7 for the "Y" variable in the 1st equation
x = 4 + Y
x = 4 + 7
x = 11.

Soooooooo one number is 7 and one number is 11.

11 is 4 greater than 7 (the smaller number) and......

3 times the smaller number (3)(7) is 21 added to 2 times the larger (2)(11) is 22, is 43.
21 + 22 = 43. Yay.

I hope this helps you.
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