# SOLUTION: Suppose you have two numbers. The difference of the two numbers is 12. The product of the two numbers is 17. Multiply the larger of the two numbers by 100, add 50 times the smaller

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 Question 75454: Suppose you have two numbers. The difference of the two numbers is 12. The product of the two numbers is 17. Multiply the larger of the two numbers by 100, add 50 times the smaller number to that, round the total to the nearest whole number and thats the answer. Found 2 solutions by checkley75, ptaylor:Answer by checkley75(3666)   (Show Source): You can put this solution on YOUR website!X-Y=12, X=Y+12 XY=17 (Y+12)Y=17 Y^2+12Y-17=0 USING THE QUADRATIC EQUATION WE GET: X=(-12+-SQRT[-12^2-4*1*-17])/2*1 X=(-12+-SQRT[144+68])/2 X=(-12+-SQRT212)/2 X=(-12+-14.56)/2 X=(-12+14.56)/2 X=2.56/2 X=1.28 ANSWER. X=(-12-14.56)/2 X=-26.56/2 X=-13.28 ANSWER. 1.28*100+(-13.28*50) 128-662.5 -535 FINAL ANSWER. Answer by ptaylor(2048)   (Show Source): You can put this solution on YOUR website!Let x=larger number And y=smaller number Now we are told that: ----------------------------------eq 1 and -----------------eq 2 We can see from a quick inspection that these two numbers are not going to be whole numbers From eq 2, . Substitute this value into eq 1 and we get: multiply each term by x subtract 12x from both sides we will solve using the quadratic formula: ----------------------------larger number We'll forget about the negative value for x because the positive value works ON SECOND THOUGHT, WE NEED TO LOOK AT THE NEGATIVE VALUE FOR X BECAUSE THIS SOLUTION WILL YIELD A DIFFERENT ANSWER. SEE BELOW: substitute into eq 1 and we get: subtract 13.2801 from both sides multiply both sides by -1 ---------------------------------smaller number CK close enough and Multiply the larger number by 100 and we get 50 times the smaller number is: Now add these two numbers together and round to the nearest whole number: Rounded to the nearest whole number we have ---------------------------------------------------answer!!! if I didn't make a mistake NOW WE WILL LOOK AT THE NEGATIVE VALUE FOR X: --------------------------larger number Substitute into eq 1: add 1.2801 to both sides multiply both sides by -1 -------------------------------------------smaller number So now we have: which equals or ------------------------another answer Hope this helps----ptaylor