a company sells seeds in either 3-pounds or 20-pound bags.e company sells 84 bags with a total weight of 660 pounds. How many 3-pound bags did the company sell?

Question

What is the equation needed to solve for thses types of problems?

Answer 1

The method used by James is a very good method. It is called the Substitution method. This problem can also be solved by the elimination or addition method. Using the same variables as James (with all due respect and permission), that is letting x be the number of 3-pound bags, and y be the number of 20-pound bags, we have the following equations:

 

x + y = 84 --------------- (1)

 

3x + 20y = 660 --------- (2)

 

Multiply any of the equations by a number such that the coefficients of the same variable term in both equations will be equal and opposite in signs.

 

Thus, multiply equation (1) by -20 to obtain:      -20x - 20y = -1680 

Bring down equation (2):                                    3x + 20y =    660

Add these two equations:                                  -17x         = -1020

 

                                                                           x = -1020/(-17) 

 

                                                                           x = 60

 

Therefore, the number of 3-pound bags sold = 60

 

Check:

 

If 60 bags of the 3-pound bags were sold, then, 24 bags (84-60) of the 20-pound bags must have been sold. Thus,

 

3(60) + 24(20) = 180 + 480

                       = 660 pounds

 

Answer 2

Let x = number of 3 pound bags

Let y = number of 20 pound bags

 

   3x + 20y = 660

   x + y = 84

 

Solve 2nd equation for x ... then substitute that expression into the first equation

 

   x = 84 - y

 

   3(84 - y) + 20y = 660

   252 - 3y + 20y = 660

   252 + 17y = 660

   17y = 660 - 252

   17y = 408

       y = 24

 

   x + y = 84

   x + 24 = 84

   x = 60

 

There were 24 of the 20 pound bags and 60 of the 3 pound bags.