Need help with this math problem please

Question

Grandma Hooper always made dumplings for her grandchildren for Sunday dinner. She made enough so that each child got three. But today, when she put the dumplings into the serving bowl, she realized that she had two dumplings more than she actually needed. Charley Hooper, was delighted. Now he and his wife could have dumplings too. and if grandma Hooper also wanted some, everybody could have two dumplings. "The children wouldn't mind getting one dumplings less, just this once," said Charlye. How many dumplings did Grandma Hooper have in the bowl when she got ready to serve? How many children are in the family? 

 

I need the answer and how did you get the answer please?

Answer 1

Hi,

 

Looks like 4 children and usually a dozen dumplings. With the extra 3 adults there are 7 to feed. If each one gets 2, then that requires 14 dumplings, which is exactly 2 more than the usual Sunday dinner.

 

d = usual number of dumplings

c = number of children 

 

Since each gets exactly 3, we have d = 3*c

 

With an extra 2 dumplings (d+2), there are enough for 2 dumplings for the children and 3 adults (c+3), so

 

d + 2 = 2*(c+3).

 

Solving gives the answer, d=12, c=4

 

Joe

 

Answer 2

Lia,

 

Let the number of children = x.  Normally grandma would make 3 dumplings for each child, so we can say:

 

3·x = N,

 

where N is the number of dumplings she would ordinarily make.  But today she made N+2 dumplings which are enough to feed 2 dumplings each to the x children, + 3 adults.  Since the number of people eating 2 dumplings each is (x+3), we can write:

 

2·(x+3) = N+2

 

Substituting for N in this 2nd equation:

 

2·(x+3) = 3·x+2

 

2·x+6 = 3·x+2

 

so x = 4

 

There are 4 children in the family:

 

Check:  3 x 4 = 12

             2 x 7 = 14 = 12+2