The sum of two numbers is 52. Their product is 100. What is the answer?

Accepted Solution

Answer: 50,2Explanation:Let’s call the two numbers a and b. The sum of them is 52 so a+b=52The product of them is 100 so ab=100We now have a system which we can solve in a variety of ways.My way: ab=100; b=100/aa+b=52; a+(100/a)=52; (a^2/a)+(100/a)=52; (a^2+100)/a=52a^2+100=52aa^2-52a+100=0This is now a quadratic which we can solve by factoring. We can use the factors -50 and -2Therefore, a^2-52a+100=(a-50)(a-2) or a equals 2 OR 50Therefore, b=(100/2) or b=(100/50) so b equals 50 OR 2 respectively.The answers are 50 and 2