Can you help me?

Question

For a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 7 acorns in each of the holes it dug. they each hid the same number of acorns, although the squirrel needed 8 fewer holes. How many acorns did the chipmunk hide?

Answer 1

Hi Brooke,

 

Denote the number of holes the chipmunk dug as c, and the number of holes the squirrel dug as s. Since the chipmunk hid 3 acorns per hole, and the squirrel 7 acorns per hole. The total number of acorns hid by the chipmunk is given as 3c, while the total number of acorns hidden by the squirrel is 7s.

 

Now, they each hid the same number of acorns, so

 

7s = 3c

 

or

 

s = (3/7) c

 

The squirrel needed 8 fewer holds, so

 

s = c - 8

 

The above equations can be set equal to obtain

 

(3/7) c = c - 8

 

Bringing like terms together, and isolating the c yields

 

8 = c - (3/7) c

 

   = (4/7) c

 

Hence, c = 8*(7/4) = 14