SOLUTION: I don't understand what to do to figure this problem out. Could someone help me please. Thank You. One number is 8 less than another. If 5 times the smaller number minus 2 times

Question 82118: I don't understand what to do to figure this problem out. Could someone help me please. Thank You.
One number is 8 less than another. If 5 times the smaller number minus 2 times the larger number is 14, find the two numbers.
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
THE ONLY SUGGESTION I CAN GIVE YOU IS TO PRACTICE PRACTICE PRACTICE. MATH/ALGEBRA/GEOMETRY IS THE SAME AS ANY OTHER LEARNING PROCESS. THE MORE YOU DO THE BETTER YOU GET & THE EASIER IT BECOMES. THERE IS NO IRON-CLAD RULE FOR THESE TYPE OF WORD PROBLEMS THAT I AM AWARE OF. HOWEVER WHAT I DO IS WRITE DOWN IN MATH TERMS EVERY PIECE OF INFORMATION GIVEN AS IT APPEARS IN THE PROBLEM & THEN FIGURE THE SIMPLEST WAY TO SOLVE FOR THE UNKNOWN(S). REMEMBVER THERE ARE GENERALLY ONLY 4 BASIC METHODS TO SOLVE PROBLEMS ADDITION, SUBTRACTION, MULTIPLICATION & DIVISION OR A COMBINATION OF THESE METHODS.
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ONE NUMBER IS 8 LESS THAN ANOTHER [X=Y-8] OR ONE NUMBER IS GREATER THAN ANOTHER
X+8=Y THESE ARE THE SAME EQUATIONS.
x=y-8
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X BEING THE SMALLER NUMBER NOW IS MULTIPLIED BY 5 (5X) MINUS 2 TIMES THE LARGER NUMBER (Y) OR (-2Y) IS = 14. NOW WE HAVE TWO EQUATIONS WITH TWO UNKNOWNS. PICK THE SIMPLEST EXPRESSION [X=Y-8] AND SUBSTITUTE & SOLVE FOR THE SINGLE UNKNOWN.
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5x-2y=14 now substitute (y-8) for x in this equation.
5(y-8)-2y=14
5y-40-2y=14
3y=14+40
3y=54
y=54/3
y=18 answer.
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NOW REPLACE Y BY 18 & SOLVE FOR THE OTHER UNKNOWN USING THE SIMPLEST FORMULA.
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x=18-8
x=10 answer.
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ALWAYS DO THE PROOF WHEN DOING HOMEWORK & DURING TESTING - IF TIME ALLOWS.
proof
5*10-2*18=14
50-36=14
14=14
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