Find 3 numbers that add to 14 when...

Algebra Level 1

Find a three-digit positive integer such that the sum of all digits is 14, twice the hundreds digit plus the tens digit equals the ones digit, and, if the digits are reversed, the new number plus the original number equals 1090?


The answer is 248.

James Cosgrove by James Cosgrove , 56

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1 solution

James Cosgrove
Feb 12, 2014

Let x = the 100's digit Let y = the 10's digit Let z = units : The original 3 digit number = 100x + 10y + z : Write an equation for each statement: : "find a three-digit positive integer such that the sum of all digits is 14," x + y + z = 14 : " twice the hundreds digit plus the tens digit equals the ones digit," 2x + y = z 2x + y - z = 0 : Use these two equation to eliminate y 2x+ y - z = 0 x + y + z = 14 -----------------Subtraction eliminates y x - 2z = -14 which is x = 2z - 14 : At this point we can see the no. of positive integers that satisfy this equation are only two z = 9, x = 4, then y = 1 z = 8, x = 2; then y = 4 : check the 2nd set of solutions (248) in the statement: "if the digits are reversed, the new number plus the original number equals 1090?" 842 + 248 = 1090 : The other set of solutions will not add up to 1090 : the 3 digit number = 248

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int temp,number,h,t,u,reverse; 

    for(temp=100;temp<=999;temp++)
    {
        number=temp;
        u=number%10;
        number=number/10;

        t=number%10;
        number=number/10;
        h=number%10;

            if((2*h+t)==u)
            {
            reverse=u*100+t*10+h;
                if(temp+reverse==1090)
                cout<<h<<"\t"<<t<<"\t"<<u<<"\n";
            }
    }

kevin j - 6 years, 10 months ago

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