An animal shelter spends $1.50 per day to care for each cat and $3.50 per day to care for each dog. Gianna noticed that the shelter spent $20.50 caring for cats and dogs on Tuesday. Gianna found a record showing that there were a total of 7 cats and dogs on Tuesday. How many cats were at the shelter on Tuesday?
Answers
Answer:
- 2 cats were cared for
Step-by-step explanation:
- c= cats
- d=dogs
- c+d =7
- 1.5c+3.5d=20.50
- c+d =7
solve for d
- d = 7-c
substitute into 1.5c+3.5d=20.50
- 1.5 c + 3.5 (7-c) = 20.50
distribute
- 1.5c +24.5 -3.5 c = 20.5
combine like terms
- 24.5 -2c =20.5
subtract 24.5 from each side
- -2c = -4
divide by -2
- c =2
Step-by-step explanation:
On Wednesday there are 22 cats at the shelter.
Step-by-step explanation:
Let c= cats and d=dogs on Wednesday, from the given question,
c + d = 29 as equation (i)
1.5c + 3.5d = 57.50 as equation (ii)
By solving (i) and (ii)
(c + d =29) × 1.5 = 1.5c + 1.5d = 43.5
(1.5c + 3.5d = 57.50) × 1 = 1.5c + 3.5d = 57.50
By solving we get d = 7
For c substitute the c value of d into 1.5c + 3.5d = 57.50
1.5 c + 3.5 (7) = 57.50
1.5c + 24.5 = 57.50
1.5 c+24.5=57.50\Rightarrow1.5 c=57.50-24.5\Rightarrow1.5 c=33 \Rightarrow c=\frac{33}{1.5}=221.5c+24.5=57.50⇒1.5c=57.50−24.5⇒1.5c=33⇒c=
1.5
33
=22
We get c = 22, d = 7
Therefore, we came to know that there were 22 cats and 7 dogs.