Four consecutive integers exist such that 2/3 of the greatest integer incresed by twenty-four is no more than the sum of the four integers. Find the smallest integer.

Question

anonymous · Answer

It's an inequality but i'm studying for finals and that was forever ago, i forgot how to do it...

zepdrix · Answer

Hmm I'm not sure if I'm doing this correctly, but I'll give you my thoughts at least :D
Let x represent the SMALLEST of the numbers, then we can think of these 4 unknown numbers as,$$\large x, \quad x+1, \quad x+2, \quad x+3$$They told us these numbers exists given some conditions.$$\large \frac{2}{3}(x+3)+24$$I think this is what is being described on the left side.
2/3 of the LARGEST number (x+3) increased by 24 NO MORE THAN (less than or equal to) the sum of the consecutive numbers.$$\large \frac{2}{3}(x+3)+24 \qquad \le \qquad x+(x+1)+(x+2)+(x+3)$$Does that look right? :D
From here they want us to solve for the smallest number, X.

anonymous · Answer

Thank you!!