Question

The cats Killer and Croaker catch mice on the waterfront. Killer has already caught 29 mice and catches 87 more mice each month. Croaker has already caught 282 mice and catches 64 more mice each month. When would they both have caught the same number of mice? How many mice would they have caught?​

Answer 1

Killer and Croaker will have caught the same number of mice after 11 months, and they will have caught a total of 1026 mice.

Step-by-step explanation:

To find the point at which Killer and Croaker have caught the same number of mice, we need to set up an equation. Let's say that x represents the number of months. The number of mice caught by Killer after x months can be represented by the equation 29 + 87x. Similarly, the number of mice caught by Croaker after x months can be represented by the equation 282 + 64x. To find the point at which they have caught the same number of mice, we need to set these two equations equal to each other and solve for x.

29 + 87x = 282 + 64x

Subtracting 64x from both sides gives:

29 + 23x = 282

Subtracting 29 from both sides gives:

23x = 253

Finally, dividing both sides by 23 gives:

x = 11.

Therefore, it will take 11 months for Killer and Croaker to have caught the same number of mice. To find the number of mice they will have caught at that point, we can substitute x = 11 into either of the original equations. Using the equation 29 + 87x, we get:

29 + 87(11) = 1026.

Therefore, Killer and Croaker will have caught the same number of mice after 11 months, and they will have caught a total of 1026 mice.