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TelstralCMOC Lebors Chis (2)

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8:41 答案详情 31 32 填空题 3 分 A person raise...

May 15, 2024

Solution by Steps

step 1

Let the initial number of dogs be

d

and the initial number of cats be

c

. Given that the total number of pets is 30 and 30% of them are dogs, we have

d = 0.3 \times 30 = 9

and

c = 30 - d = 21

step 2

Let

x

be the number of extra dogs raised. After raising

x

extra dogs, the total number of dogs becomes

d + x = 9 + x

and the total number of pets becomes

30 + x

step 3

Given that the proportion of dogs becomes 50%, we set up the equation

\frac{9 + x}{30 + x} = 0.5

step 4

Solving for

x

, we get:

\frac{9 + x}{30 + x} = 0.5 \implies 9 + x = 0.5(30 + x) \implies 9 + x = 15 + 0.5x \implies 0.5x = 6 \implies x = 12

So, 12 extra dogs are raised

step 5

Now, the total number of pets is

30 + 12 = 42

and the number of dogs is

9 + 12 = 21

step 6

To bring the proportion of dogs back to 30%, let

y

be the number of new cats needed. The total number of pets becomes

42 + y

and the number of dogs remains 21. We set up the equation

\frac{21}{42 + y} = 0.3

step 7

Solving for

y

, we get:

\frac{21}{42 + y} = 0.3 \implies 21 = 0.3(42 + y) \implies 21 = 12.6 + 0.3y \implies 0.3y = 8.4 \implies y = 28

So, 28 new cats need to be raised

Answer

Key Concept

Proportion of dogs and total number of pets

Explanation

To find the number of new cats needed to bring the proportion of dogs back to 30%, we first determine the number of extra dogs raised and then solve for the number of new cats required to adjust the proportion.