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Solved on Oct 25, 2023

There are 40 fish in a pond. 1212 are bream, 14\frac{1}{4} of the remaining are tench, and the rest are carp. Find the ratio of bream:tench:carp.

STEP 1

Assumptions1. The total number of fish in the pond is40. . The number of bream in the pond is12.
3. Of the fish that are not bream, 14\frac{1}{4} are tench and the rest are carp.

STEP 2

First, we need to find the number of fish that are not bream. We can do this by subtracting the number of bream from the total number of fish.
Number of non−bream fish=Total number of fish−Number of breamNumber\, of\, non-bream\, fish = Total\, number\, of\, fish - Number\, of\, bream

STEP 3

Now, plug in the given values for the total number of fish and the number of bream to calculate the number of non-bream fish.
Number of non−bream fish=40−12Number\, of\, non-bream\, fish =40 -12

STEP 4

Calculate the number of non-bream fish.
Number of non−bream fish=40−12=28Number\, of\, non-bream\, fish =40 -12 =28

STEP 5

Now that we have the number of non-bream fish, we can find the number of tench. We can do this by multiplying the number of non-bream fish by 14\frac{1}{4}.
Number of tench=Number of non−bream fishtimes14Number\, of\, tench = Number\, of\, non-bream\, fish \\times \frac{1}{4}

STEP 6

Plug in the value for the number of non-bream fish to calculate the number of tench.
Number of tench=28times14Number\, of\, tench =28 \\times \frac{1}{4}

STEP 7

Calculate the number of tench.
Number of tench=28times14=7Number\, of\, tench =28 \\times \frac{1}{4} =7

STEP 8

Now that we have the number of tench, we can find the number of carp. We can do this by subtracting the number of tench from the number of non-bream fish.
Number of carp=Number of non−bream fish−Number of tenchNumber\, of\, carp = Number\, of\, non-bream\, fish - Number\, of\, tench

STEP 9

Plug in the values for the number of non-bream fish and the number of tench to calculate the number of carp.
Number of carp=28−7Number\, of\, carp =28 -7

STEP 10

Calculate the number of carp.
Number of carp=28−7=21Number\, of\, carp =28 -7 =21

STEP 11

Now that we have the number of each type of fish, we can find the ratio of bream to tench to carp. This can be done by writing the numbers of each type of fish as a ratio.
Ratio of bream to tench to carp=Number of breamNumber of tenchNumber of carpRatio\, of\, bream\, to\, tench\, to\, carp = Number\, of\, bream Number\, of\, tench Number\, of\, carp

STEP 12

Plug in the values for the number of bream, tench, and carp to write the ratio.
Ratio of bream to tench to carp=12721Ratio\, of\, bream\, to\, tench\, to\, carp =12721The ratio of bream to tench to carp in the pond is12721 in its simplest form.

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