Find the number of cans of popcorn and the number of mixed nuts sold.

Question

Suppose the band sells cans of popcorn for $5 per can and can of mixed nuts for $8 per can.  The band sells 240 cans and receives a total of $1614.

Answer 1

You are being asked to find two variables (number of cans of popcorn and number of cans of nuts). When you have two variables, you need two equations. Let's write one for the number of cans and another for the total sales. Your Algebra teacher might call this a "system of equations."

 

Let p equal the number of cans of popcorn and n stand for the number of cans of nuts.

 

p + n = 240 cans

5p + 8n = $1614

 

You can use a variety of methods to find the values of p and n, such as elimination, substitution, or graphing. 

Let's us elimination because it's easier to display in this forum.

 

Take the first equation and write p in terms of n.

p + n = 240

    - n     - n     Subtract n from both sides

p = 240 - n

 

Use "240 - n" for p in the second equation.

5(240 - n) + 8n = 1614

1200 - 5n + 8n = 1614   Distribute

3n + 1200 = 1614          Combine like terms

     - 1200     -1200         Subtract 1200 from both sides

3n = 414          

/3     /3                          Divide both sides by 3

n = 138

 

So there were 138 cans of nuts sold.

 

Plug this into the first equation and solve for p.

p = 240 - n

p = 240 - 138     Plug in the value of n

p = 102

 

So, there were 102 cans of popcorn sold.

 

Remember to check that your answer makes sense. Re-read the original problem to see that the values work.

Answer 2

Hi Sierra,

 

Let N = number of cans of nuts sold

 

and P = number of cans of popcorn sold

 

N + P = 240 ,  The total number of cans N+P is 240 sold

 

5N + 8P = 1614 , The 240 cans sold for $1614, and they are priced at $5 for nuts or 5N and  $8 for popcorn or 8P

 

now simply solve the two equations.

 

we can multiply equation 1 by 5 to get

 

   5N + 5P = 1200 ,  and then subtract the second equation from it

 

-(5N + 8P = 1614) , to give

 

-3P = -414

 

P=138 , plug that back into the first equation to get

 

N=102