Mathematics, 15.02.2020 06:54 MayFlowers

An animal shelter spends $3.00 per day to care for each cat and $5.50 per day to care for each dog. Layla noticed that the shelter spent $57.50 caring for cats and dogs on Monday. Layla found a record showing that there were a total of 15 cats and dogs on Monday. How many cats were at the shelter on Monday?

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Answer from: 3peak101

Step-by-step explanation:

If all were dogs, the expense would have been ...

$5.50 × 15 = $82.50

The actual expense was less by ...

$82.50 -57.50 = $25.00

Each cat costs $2.50 per day less than a dog, so there must have been ...

$25.00/$2.50 = 10 . . . . cats in the shelter on Monday

If you write an equation for the number of cats, it might look like ...

3.00c +5.50(15 -c) = 57.50

-2.50c +82.50 = 57.50 . . . . . eliminate parentheses, collect terms

-2.50c = -25.00 . . . . . . . . . . . subtract 82.50

c = -25.00/-2.50 = 10 . . . . . . the number of cats on Monday

Comment on the question

All of your "animal shelter" questions can be answered the same way. Use a variable for the number of one kind of animal, and use the difference from the total as the number of the other animal. Write an equation for the total cost, as we have done here. The solution takes about 3 steps, as here.

You will note that the "word solution" presented first is fully equivalent to the equation solution.

If you make the variable represent the highest-cost animal, the numbers will remain positive. Here, the question asked for the number of cats, the lower-cost animal, so we saw some negative numbers in the solution.

Answer from: lucyfox8165

10 cats were at the shelter on Monday.

Step-by-step explanation:

Let x represent the number of cats were at the shelter on Monday.

Let y represent the number of dogs were at the shelter on Monday.

Layla found a record showing that there were a total of 15 cats and dogs on Monday. This means that

x + y = 15

The animal shelter spends $3.00 per day to care for each cat and $5.50 per day to care for each dog. Layla noticed that the shelter spent $57.50 caring for cats and dogs on Monday. This means that

3x + 5.5y = 57.5 - - - - - - - - - - - - -1

Substituting x = 15 - y into equation 1, it becomes

3(15 - y) + 5.5y = 57.5

45 - 3y + 5.5y = 57.5

- 3y + 5.5y = 57.5 - 45

2.5y = 12.5

y = 12.5/2.5

y = 5

x = 15 - y = 15 - 5

x = 10

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An animal shelter spends $3.00 per day to care for each cat and $5.50 per day to care for each dog....

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