Tommy had 35 more bugs than Diego. They had 103 bugs altogether. When Diego lost some bugs, Tommy had 3 times as many as Diego. How many bugs had Diego lost?
To solve this problem, let's break it down step by step:
1. Let's assume the number of bugs Diego had as "x".
2. Tommy had 35 more bugs than Diego, so Tommy would have "x + 35" bugs.
3. Together, they had 103 bugs, so we can form an equation: x + (x + 35) = 103.
4. Simplifying the equation, we have: 2x + 35 = 103.
5. To isolate "x," we subtract 35 from both sides of the equation: 2x = 103 - 35.
This gives us the equation: 2x = 68.
6. Finally, to find the value of "x," we divide both sides of the equation by 2: x = 68/2.
This gives us the solution: x = 34.
So, Diego originally had 34 bugs.
Now, we need to find out how many bugs Diego lost when Tommy had three times as many as Diego:
1. When Tommy had three times as many bugs as Diego, Tommy had 3 * x = 3 * 34 = 102 bugs.
2. We know that Tommy and Diego had a total of 103 bugs at some point, so we can find out how many bugs Diego lost by subtracting Tommy's new number of bugs from the original total: 103 - 102 = 1.
Therefore, Diego lost 1 bug.