If 26 Blims weigh as much as 4 Blams and 2 Blums while 8 Blims and 2 Blams have the same weight as 2 Blums, how many Blims have the same weight as 3 Blums?
To solve this problem, we need to analyze the information given and set up equations that represent the given relationships.
Let's assign variables to the unknown quantities. Let's say the weight of a Blim is B, and the weight of a Blam is M, and the weight of a Blum is U.
According to the given information:
- 26 Blims weigh as much as 4 Blams and 2 Blums. This can be represented as: 26B = 4M + 2U.
- Also, 8 Blims and 2 Blams have the same weight as 2 Blums. This can be represented as: 8B + 2M = 2U.
Now, we need to find the number of Blims that weigh the same as 3 Blums. Let's call the number of Blims we are looking for as X.
We know that 1 Blim weighs the same as 1/2 Blam and 1/13 Blum (from the first equation). So, to find X Blims that weigh the same as 3 Blums, we need to multiply both sides of the equation by X. This gives:
26X B = 4X/2 M + 2X/13 U
Simplifying the above equation, we get:
26X B = 2X M + 2X/13 U
Now, we can rewrite the second equation by multiplying both sides by 4:
40B + 8M = 8U
Now, we can substitute the value of M in the above equation using the first equation:
40B + (26B - 2U) = 8U
Simplifying the equation above:
66B - 2U - 8U = 0
66B - 10U = 0
Therefore, we can solve this equation to find the ratio of B to U:
66/10 = B/U
6.6 = B/U
So, for every 6.6 Blims, we have 1 Blum.
Now, we can put this ratio into the equation we obtained earlier:
26X B = 2X M + 2X/13 U
26X B = 2X M + 2X/13 (6.6 B)
26X B = 2X M + X/10 B
Dividing both sides by B:
26X = 2X/10 + X/10
Multiplying both sides by 10:
260X = 2X + X
260X = 3X
Dividing both sides by X:
260 = 3
This equation is absurd since there is no solution. Therefore, there is no number of Blims that weigh the same as 3 Blums according to the given information.