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In the first week of January, there are 49 dogs and 28 cats in an animal shelter. Throughout the month, the ratio of dogs to cats remains the same. In the last week of January, there are 20 cats in the shelter. How many dogs are there?

Sagot :

MrRoyalidn

Answer:

35 dogs

Step-by-step explanation:

Given

[tex]49\ dogs: 28\ cats[/tex]

Required

Determine the number of dogs for 20 cats

Represent the required number of dogs as a ratio of number of cats

[tex]x : 20\ cats[/tex]

So, we have:

[tex]49\ dogs: 28\ cats[/tex]

[tex]x : 20\ cats[/tex]

Since, the ratio is the same throughout, we have:

[tex]x : 20\ cats[/tex] = [tex]49\ dogs: 28\ cats[/tex]

Convert ratio to fraction

[tex]\frac{x}{20} = \frac{49}{28}[/tex]

[tex]\frac{x}{20} = \frac{7}{4}[/tex]

Multiply through by 20

[tex]x = \frac{7}{4} * 20[/tex]

[tex]x = 7 * 5[/tex]

[tex]x = 35[/tex]

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