SOLUTION: The sum of a first and second number is 216 less than 400. Six times the first number decreased by 400 is equal to two times the second number plus 24. Find the two numbers

Question 25579: The sum of a first and second number is 216 less than 400. Six times the first number decreased by 400 is equal to two times the second number plus 24. Find the two numbers
Answer by 641387213(2) (Show Source): You can put this solution on YOUR website!
Since we don't know what the numbers are, let's say "X" is one of the numbers and "Y" is the other.
1. X + Y = 400 - 216 or
2. X + Y = 184
1. 6X - 400 = 2Y + 24...At this point you're going to try to isolate(leave alone) the X and the Y together. So you must add the -400,on the left side, by +400,
or -400 + 400 = 0 (400 - 400 = 0)
2. Now, since you added the 400 on the left side, you must do the same on the right side. 24 + 400 = 424
3. So far we have, 6X = 2Y + 424. Now, to isolate the X and Y, Subtract 2Y from the "2Y" on the left. 2Y - 2Y = 0.
4. Since you subtracted 2Y from the left side, you must now add it to the right side. 6X + 2Y = 424
5. Now what number can be divided by 6X + 2Y ?...2(3X = Y)...Divide 6X by 2 = 3X, and 2Y by 2 = Y, that's how you get 2(3X + Y).
6. Since your multiplying the "2" by "(3X + Y)", you also divide it.
7. Since you divided it from the left side, you must divide it from the right. 424 divided by 2 = 212
8. So far we have 3X + Y = 212. Now let's return to #2 on the very top: X + Y = 184... Now you figure out what two numbers fill those slots (X and Y).
9. Now "you" find out X and Y . Remember: 3X + Y = 212 and X + Y = 184 (hint: one of the numbers turned around is 48)
^_^
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