Need help with these problems! (Process of Elmination)

Question

An animal shelter spends $3.00 per day to care for each cat and $6.00 per day to care for each dog. Colton noticed that the shelter spent $180.00 caring for cats and dogs on Monday. Colton found a record showing that there were a total of 42 cats and dogs on Monday. How many cats were at the shelter on Monday?

 

Ramsay and Levi go to the movie theater and purchase refreshments for their friends.

Ramsay spends a total of $28.25 on 3 drinks and 7 bags of popcorn.

Levi spends a total of $61.50 on 15 drinks and 6 bags of popcorn.

Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.

Using these equations, determine and state the price of a drink, to the nearest cent.

 

A bag contains white marbles and green marbles, 55 in total. The number of white marbles is 5 less than 4 times the number of green marbles. How many white marbles are there?

Answer 1

I'm going to work through the first one and let you use this logic to solve the 2nd and 3rd ones.

 

Let C = # cats

D = # dogs

 

  C  +  D =   42

3C + 6D = 180

 

Let's multiply the first equation by 3 so that both equations have a 3C term

 

3C + 3D = 126

3C + 6D = 180

 

Subtract the 1st equation from the 2nd equation (or you can subtract the 2nd equation from the first).  This will eliminate the C term.

 

3D = 54

D = 18

 

Now use D=18 in the first equation to solve for C

C + D = 42

C + 18 + 42

C = 24

 

Use this logic to solve the other problems.