How do I figure out what the two wole numbers whose product is 1224 and whose sum is 70 is?

Question

anonymous · Answer

simultaneous equations

anonymous · Answer

??

watchmath · Answer

36 and 34 I guess :)

anonymous · Answer

Think of all the numbers that add up to 70, then multiply the pairs untill you find one that = 1224 .

anonymous · Answer

Thank you. I can figure it out that way but wasn't sure if there was a alegbra fomula for this?

watchmath · Answer

Use intellegent guess. 40 times 30 is 1200. So the two numbers roughly between 30 and 40. To make the sum 70 and the last digit equal 4, we need the two end digits to be 4 and 6. Hence the best bet is 34,36. Checking the product of the two confirm our guess.

watchmath · Answer

If you want to solve this algebraically:
$x+y=70$
$xy=1224$
$x(70-x)=1224$
$-x^2+70x-1224=0$
Use quadratic formula to solve it for x.