please help

Question

Mrs. Parker is planning to organize a party. She wants to purchase hamburgers and hot dogs for the party. The hamburgers come in packages of 10, and the hot dogs come in packages of 11. She wants to purchase an amount that will not leave any extra hamburger or hot dog.

What amount will not leave any extra hamburger or hot dog?

 

Mrs Parker decides that she will need enough hamburgers with hot dogs to serve 310 people, but she still wants to have an equal number of hamburgers and hot dogs. Decide which amount of the following she will need.

Total number of hamburgers with hot dogs:


Packages of hamburgers:

Packages of hot dogs:

Answer 1

Ken, 

 

This one needs to be taken in stages as it has multiple required answers.

 

To begin, you need to find the numerical value where X number of hotdog packages matches Y number of hamburger packages without splitting a package.  To do this, find the common multiplier between 10 and 11.  Since there is no number that divides both 10 and 11, they multiply.

 

IE:  10 packs of (11)hot dogs and 11 packs of (10)hot dogs will have an equal number of items.

 

This is the answer for the first question.

 

 

Now, we need to take this answer and expand it to include at least 310 people.  The question does not state whether each person needs one item or one of each, so we will assume that each person needs (1) hot dog and (1) hamburger.  

 

Since 110 hotdogs/hamburgers is the lowest common amount, we need to figure out how many of this 'lowest amount' is required.  

 

110 x 3 = 330 which is greater than 310.

 

Now, If you have 330 hotdogs and 330 hamburgers, how many packages of each do you need?

 

Hmaburgers:

1/10=X/330

 

Hotdogs:

1/11=X/330

 

 

I'll leave the last steps for you.

 

Answer 2

This is a Least Common Multiple (LCM) problem. The LCM of two numbers is the smallest number that both of them will evenly divide into. If the two numbers have no common factors (The same number won't evenly divide into them), then the LCM is just the product of the two numbers.

 

Since no number (other than 1, which doesn't count) will evenly divide into both 10 and 11, the LCM is just 10x11 = 110.

So she needs 11 packages of hamburgers and 10 packages of hot dogs.

 

For the second part, to feed 310 people, she needs some multiple of 110, which would be 330 total, or

33 packages of hamburgers and 30 packages of hot dogs.