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, we need to set up equations based on the given information.
Let's say the number of bugs Diego had is represented by the variable "x".
According to the first sentence, Tommy had 35 more bugs than Diego, so Tommy had a total of "x + 35" bugs.
The second sentence states that the total number of bugs they had altogether is 103, so the equation becomes:
x + (x + 35) = 103
Simplifying this equation, we get:
2x + 35 = 103
2x = 103 - 35
2x = 68
x = 34
So, Diego had 34 bugs initially.
According to the third sentence, Tommy had 3 times as many bugs as Diego when Diego lost some bugs. Let's say Diego lost "y" bugs.
After losing "y" bugs, Diego had x - y bugs.
At the same time, Tommy had 3 times as many bugs as Diego, so Tommy had 3(x - y) bugs.
According to the problem, Tommy ended up having 3 times as many bugs as Diego, so:
3(x - y) = x - y + 35
Simplifying this equation, we get:
3x - 3y = x - y + 35
2x - 2y = 35
2(x - y) = 35
x - y = 35/2
x - y = 17.5
Since we are dealing with bugs, the number of lost bugs must be a whole number. Therefore, Diego couldn't have lost 17.5 bugs.
In this case, there seems to be an inconsistency or an error in the problem. Please double-check the given information to ensure accuracy.