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Madeleine keeps a record of how many fish she catches each month. Last month she caught three types of fish: perch bream and minnow. The ratio of perch to bream was 7:12 The ratio of bream to minnow was 4:3 What is the smallest number of fish she could have caught last month?

Question

Madeleine keeps a record of how
many fish she catches each month.
Last month she caught three types
of fish: perch bream and minnow.
The ratio of perch to bream was
7:12
The ratio of bream to minnow was
4:3
What is the smallest number of fish
she could have caught last month?

Madeleine keeps a record of how many fish she catches each month. Last month she caught three types of fish: perch bream and minnow. The ratio of perch to bream was 7:12 The ratio of bream to minnow was 4:3 What is the smallest number of fish she could have caught last month?

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Answer

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OliverElite · Tutor for 8 years

Answer

28

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## Step1:<br />First, we need to find a common number for bream in both ratios. The common number is the least common multiple (LCM) of the two numbers. The LCM of 12 and 4 is 12.<br /><br />## Step2:<br />Now, we adjust the ratios to have the same number for bream. The ratio of perch to bream becomes \(7:12\) and the ratio of bream to minnow becomes \(12:9\).<br /><br />## Step3:<br />We can now combine these ratios to get the ratio of perch to bream to minnow, which is \(7:12:9\).<br /><br />## Step4:<br />The smallest number of fish she could have caught last month is the sum of the numbers in the combined ratio, which is \(7 + 12 + 9 = 28\).
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