Question

A tank contains fish, crabs and shells. The number of fish is four fifths of the number of crabs. The number of shells is eleven tenths of the number of crabs. What is the ratio of fish, crabs and shells expressed in its lowest terms ?

Answer 1

To find the ratio of fish, crabs, and shells, set up equations based on the given information. Simplify the equations and find the common ratio.

Step-by-step explanation:

To find the ratio of fish, crabs, and shells, we need to set up equations based on the given information. Let the number of crabs be represented by C. According to the first statement, the number of fish is four fifths of the number of crabs, so the number of fish can be represented by 4C/5. According to the second statement, the number of shells is eleven tenths of the number of crabs, so the number of shells can be represented by 11C/10.

Now, we need to put the three quantities together. Since the sum of the ratios should be 1 (since it represents the total), we have the equation 4C/5 + C + 11C/10 = C. We can simplify this equation to get 8C + 10C + 11C = 10C, which can be further simplified to 29C = 10C.

Therefore, the ratio of fish, crabs, and shells is 4/5 : 1 : 11/10, or simplifying it, 8 : 10 : 11.