Math / Numbers & Operations

Question12) The ratio of dogs to cats at the local animal shelter is 5 to 4 . If there are 20 cats in the shelter, how many total animals are in the shelter?
Proportion: - $\qquad$ $=$ $\qquad$

Studdy Solution

STEP 1

1. The ratio of dogs to cats is $5$ to $4$ .
2. There are $20$ cats in the shelter.
3. We need to find the total number of animals in the shelter.

STEP 2

1. Define the variables.
2. Set up a proportion.
3. Solve the proportion.
4. Calculate the total number of animals.

STEP 3

Let $d$ be the number of dogs in the shelter.

STEP 4

Set up the proportion using the given ratio and the number of cats.
$\frac{5 \text{ dogs}}{4 \text{ cats}} = \frac{d \text{ dogs}}{20 \text{ cats}}$

STEP 5

Solve the proportion for $d$ .
Multiply both sides by $20$ to isolate $d$ .
$\frac{5}{4} = \frac{d}{20}$ $(20)\left(\frac{5}{4}\right) = \left(\frac{d}{20}\right)(20)$ $(20)\left(\frac{5}{4}\right) = d$

STEP 6

Calculate the number of dogs:
$(20)\left(\frac{5}{4}\right) = \frac{100}{4} = 25$
Thus, there are $25$ dogs in the shelter.

STEP 7

Calculate the total number of animals in the shelter by adding the number of dogs and cats.
$\text{Total animals} = 25 \text{ dogs} + 20 \text{ cats} = 45 \text{ animals}$
The total number of animals in the shelter is:
$\boxed{45 \text{ animals}}$

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Question12) The ratio of dogs to cats at the local animal shelter is 5 to 4 . If there are 20 cats in the shelter, how many total animals are in the shelter?
Proportion: - $\qquad$ $=$ $\qquad$

Studdy Solution

STEP 1

1. The ratio of dogs to cats is $5$ to $4$ .
2. There are $20$ cats in the shelter.
3. We need to find the total number of animals in the shelter.

STEP 2

1. Define the variables.
2. Set up a proportion.
3. Solve the proportion.
4. Calculate the total number of animals.

STEP 3

Let $d$ be the number of dogs in the shelter.

STEP 4

Set up the proportion using the given ratio and the number of cats.
$\frac{5 \text{ dogs}}{4 \text{ cats}} = \frac{d \text{ dogs}}{20 \text{ cats}}$

STEP 5

Solve the proportion for $d$ .
Multiply both sides by $20$ to isolate $d$ .
$\frac{5}{4} = \frac{d}{20}$ $(20)\left(\frac{5}{4}\right) = \left(\frac{d}{20}\right)(20)$ $(20)\left(\frac{5}{4}\right) = d$

STEP 6

Calculate the number of dogs:
$(20)\left(\frac{5}{4}\right) = \frac{100}{4} = 25$
Thus, there are $25$ dogs in the shelter.

STEP 7

Calculate the total number of animals in the shelter by adding the number of dogs and cats.
$\text{Total animals} = 25 \text{ dogs} + 20 \text{ cats} = 45 \text{ animals}$
The total number of animals in the shelter is:
$\boxed{45 \text{ animals}}$

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Question12) The ratio of dogs to cats at the local animal shelter is 5 to 4 . If there are 20 cats in the shelter, how many total animals are in the shelter?Proportion: - \qquad === \qquad

Studdy Solution

STEP 1

1. The ratio of dogs to cats is 5 5 5 to 4 4 4.2. There are 20 20 20 cats in the shelter.3. We need to find the total number of animals in the shelter.

STEP 2

1. Define the variables.2. Set up a proportion.3. Solve the proportion.4. Calculate the total number of animals.

STEP 3

Let d d d be the number of dogs in the shelter.

STEP 4

Set up the proportion using the given ratio and the number of cats.5 dogs4 cats=d dogs20 cats\frac{5 \text{ dogs}}{4 \text{ cats}} = \frac{d \text{ dogs}}{20 \text{ cats}}4 cats5 dogs​=20 catsd dogs​

STEP 5

Solve the proportion for d d d.Multiply both sides by 20 20 20 to isolate d d d.54=d20\frac{5}{4} = \frac{d}{20}45​=20d​ (20)(54)=(d20)(20)(20)\left(\frac{5}{4}\right) = \left(\frac{d}{20}\right)(20)(20)(45​)=(20d​)(20) (20)(54)=d(20)\left(\frac{5}{4}\right) = d(20)(45​)=d

STEP 6

Calculate the number of dogs:(20)(54)=1004=25(20)\left(\frac{5}{4}\right) = \frac{100}{4} = 25(20)(45​)=4100​=25Thus, there are 25 25 25 dogs in the shelter.

STEP 7

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Question12) The ratio of dogs to cats at the local animal shelter is 5 to 4 . If there are 20 cats in the shelter, how many total animals are in the shelter?
Proportion: - $\qquad$ $=$ $\qquad$

1. The ratio of dogs to cats is $5$ to $4$ .
2. There are $20$ cats in the shelter.
3. We need to find the total number of animals in the shelter.

1. Define the variables.
2. Set up a proportion.
3. Solve the proportion.
4. Calculate the total number of animals.

Let $d$ be the number of dogs in the shelter.

Set up the proportion using the given ratio and the number of cats.
$\frac{5 \text{ dogs}}{4 \text{ cats}} = \frac{d \text{ dogs}}{20 \text{ cats}}$

Solve the proportion for $d$ .
Multiply both sides by $20$ to isolate $d$ .
$\frac{5}{4} = \frac{d}{20}$ $(20)\left(\frac{5}{4}\right) = \left(\frac{d}{20}\right)(20)$ $(20)\left(\frac{5}{4}\right) = d$

Calculate the number of dogs:
$(20)\left(\frac{5}{4}\right) = \frac{100}{4} = 25$
Thus, there are $25$ dogs in the shelter.