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Jim Kim Mim and Tim all went fishing. They each caught one fish. They measured each fish to the nearest inch and weighed them to the nearest pound. When they lined the fish up end to end they stretched from one edge of the 6-foot-long table to the other. The four fish weighed a total of 20 pounds. Tim's fish was the longest and one of only two fish that were of equal weight. Jim's fish was one inch shorter than Tim's and one inch longer than Kim's. Kim's fish was the shortest and lightest. It weighed a full two lbs less than Mim's. The weight of Jim's and Tim's fish combined was the same as Mim's and Kim's two fish combined. The shortest fish was 1 foot 5 inches long. What was the weight (in pounds) and length (in inches) of each person's fish(?)
I can't figure this one out. Please help!
Let the lengths in inches be represented by the uppercase initials, J,K,M,T, and the weights in pounds by the lowercase initials, j,k,m,t.
J+K+M+T=72 ....(1)
j+k+m+t=20 ....(2)
T-J=1 ....(3)
J-K=1 ....(4)
m-k=2 ....(5)
j+t=m+k ...(6)
use(2) to conlude that
j+t=m+k=10 ....(6A)
From m-k=2 and m+k=2, calculate m and k.
"Tim's fish was the longest and one of only two fish that were of equal weight." =>
t≠m, otherwise j=k.
Likewise, t≠k, otherwise j=m.
Therefore t=j=5
The shortest fish was 1 foot 5 inches (17") long. =>
T+J+K=17"+18"+19"=54
M=72-54=18
Read and understand the above carefully, solve for all the variables, and post if you have questions.
Let's break down the given information step by step to find the weight and length of each person's fish.
1. We know that the length of the shortest fish is 1 foot 5 inches.
2. Let's assign variables to each person's fish:
- Jim's fish length = J (in inches)
- Kim's fish length = K (in inches)
- Mim's fish length = M (in inches)
- Tim's fish length = T (in inches)
- Jim's fish weight = WJ (in pounds)
- Kim's fish weight = WK (in pounds)
- Mim's fish weight = WM (in pounds)
- Tim's fish weight = WT (in pounds)
3. From the given information, we know:
- Jim's fish length = Tim's fish length + 1 inch
- Jim's fish length = Kim's fish length + 2 inches
- Kim's fish length is the shortest
Using these three statements, we can express all the fish lengths in terms of Kim's fish length (K):
Jim's fish length = K + 2 inches
Tim's fish length = K + 1 inch
Mim's fish length = K - 1 inch
4. The total length of all the fish lining up end to end is 6 feet, which is 72 inches. So, we can write the equation:
K + 2 + (K + 1) + K + (K - 1) = 72
Simplifying this equation, we get:
4K + 2 = 72
4K = 70
K = 17.5
Therefore, Kim's fish length is 17.5 inches.
5. Now, we can substitute the values of Kim's fish length into the expressions for Jim's, Tim's, and Mim's fish lengths:
Jim's fish length = 17.5 + 2 = 19.5 inches
Tim's fish length = 17.5 + 1 = 18.5 inches
Mim's fish length = 17.5 - 1 = 16.5 inches
6. We know that Jim's and Tim's fish combined weigh the same as Mim's and Kim's two fish combined. Let's express this as an equation:
WJ + WT = WM + (WK * 2)
7. We also know that the total weight of all four fish is 20 pounds. So, we can write another equation:
WJ + WK + WM + WT = 20
8. From the given information, we know that Mim's fish weighs 2 pounds less than Mim's fish. So, we can write another equation:
WM = WK - 2
9. Now, let's solve the equations:
From equation (8), we have: WM = WK - 2
Substituting this into equation (6), we get: WJ + WT = (WK - 2) + (WK * 2)
Simplifying this equation, we get: WJ + WT = 2WK
From equation (9), we have: WJ + WK + WM + WT = 20
Substituting equation (8) into this, we get: WJ + WK + (WK - 2) + WT = 20
Simplifying this equation, we get: WJ + 2WK + WT = 22
Now, we have a system of equations:
WJ + WT = 2WK (equation 1)
WJ + 2WK + WT = 22 (equation 2)
10. Let's solve the system of equations:
Subtracting equation (1) from equation (2), we get: (WJ + 2WK + WT) - (WJ + WT) = 22 - 2WK
Simplifying this equation, we get: WK = 22 - 2
WK = 20
Substituting this value back into equation (1), we have: WJ + WT = 2 * 20
WJ + WT = 40
11. We have two equations now:
WJ + WT = 40 (equation 3)
WK = 20 (equation 4)
12. Let's solve the system of equations again:
Subtracting equation (4) from equation (3), we get: (WJ + WT) - 20 = 40 - 20
WJ + WT = 20
From this equation, we can tell that WJ = 20 - WT.
13. Given that the weight of Jim's and Tim's fish combined is 20 pounds, we know that Jim's fish cannot weigh more than 10 pounds because the combined weight cannot exceed 20 pounds. Similarly, Tim's fish cannot weigh more than 10 pounds.
14. We have determined that the fish weights for Jim and Tim cannot exceed 10 pounds. Let's try different weight combinations for them to find the unique solution:
- If Jim's fish weighs 9 pounds (WJ = 9), then Tim's fish must weigh 11 pounds (WT = 11). Substituting these values into equation (3), we get: 9 + 11 = 20 (satisfied).
- If Jim's fish weighs 8 pounds (WJ = 8), then Tim's fish must weigh 12 pounds (WT = 12). Substituting these values into equation (3), we get: 8 + 12 = 20 (satisfied).
15. We have two possible solutions:
Solution 1:
Jim's fish weight = 9 pounds
Tim's fish weight = 11 pounds
Solution 2:
Jim's fish weight = 8 pounds
Tim's fish weight = 12 pounds
16. Now, let's summarize the findings:
Solution 1:
- Jim's fish length = 19.5 inches
- Tim's fish length = 18.5 inches
- Kim's fish length = 17.5 inches
- Mim's fish length = 16.5 inches
- Jim's fish weight = 9 pounds
- Tim's fish weight = 11 pounds
- Kim's fish weight = 20 pounds
- Mim's fish weight = 18 pounds
Solution 2:
- Jim's fish length = 19.5 inches
- Tim's fish length = 18.5 inches
- Kim's fish length = 17.5 inches
- Mim's fish length = 16.5 inches
- Jim's fish weight = 8 pounds
- Tim's fish weight = 12 pounds
- Kim's fish weight = 20 pounds
- Mim's fish weight = 18 pounds
Therefore, there are two possible solutions for the weight and length of each person's fish.
To solve this problem, we need to gather all the given information and carefully analyze it step by step. Let's break down the information and use variables to represent the unknowns.
1. Tim's fish is the longest, and one of only two fish that are of equal weight.
Let's represent Tim's fish's weight as T and length as TL.
2. Jim's fish is one inch shorter than Tim's fish and one inch longer than Kim's fish.
Represent Jim's fish's weight as J and length as JL.
Since Jim's fish is one inch shorter than Tim's, we can say JL = TL - 1.
And since Jim's fish is one inch longer than Kim's, we can say JL = KL + 1.
3. Kim's fish is the shortest and lightest. It weighs two pounds less than Mim's fish.
Represent Kim's fish's weight as K and length as KL.
Since Kim's fish is the shortest, we know KL = 17 inches (1 foot 5 inches).
And since Kim's fish weighs two pounds less than Mim's, we can say K = M - 2.
4. The combined weight of Jim's and Tim's fish is the same as the combined weight of Mim's and Kim's fish.
So J + T = M + K.
5. The total weight of all four fish is 20 pounds.
So J + T + M + K = 20.
Now, using the given information and the variables we've introduced, we can solve the system of equations.
From statements 2 and 3, we have JL = KL + 1 and KL = 17. Therefore, JL = 17 + 1 = 18 inches.
From statements 4 and 5, we have J + T = M + K and J + T + M + K = 20. Substituting the values we found so far, we get (JL - 1) + TL + (JL + 1) + 17 = 20.
Combining like terms, we have 2JL + TL = 20 - 17 = 3.
Now, let's substitute the value of JL we found earlier (18) into this equation: 2(18) + TL = 3. Simplifying further, we have 36 + TL = 3. Subtracting 36 from both sides, we get TL = -33. However, this doesn't make sense as length cannot be negative.
Therefore, it seems there may be an error or inconsistency in the problem statement. Double-check the information and ensure it's accurate. If you find any mistakes or contradictions, please correct them, and I'll be happy to assist you further in solving the updated problem.