A package delivery service delivered 30 packages. Each package weighed either 5 or 8 pounds. If the total weight of all of the packages was 186 pounds, how many

Question

A package delivery service delivered 30 packages. Each package weighed either 5 or 8 pounds. If the total weight of all of the packages was 186 pounds, how many 8 pound packages were there ?

Answer 1

Let the number of 5lb packages be X and the number of 8lb packages be Y.

 

The total weight of all packages is 186lb. This means X number of 5lb packages plus Y number of 8lb packages should equal 186. 

 

Thus: 5X + 8Y = 186.

 

The total number of packages is 30 which means X plus Y makes 30.

 

Thus: X + Y = 30

 

Now we have 2 equations.  Let us solve the 2nd equation for X given that our actual interest is in how many 8lb packages there were i.e. We want to know what Y is.

 

X + Y = 30.

 

Subtract Y from both sides and we get:

 

X + Y - Y = 30 - Y

 

X = 30 - Y

 

Now replace "X" with "30 - Y" in the first equation.

 

5X + 8Y = 186

 

5(30 - Y) + 8Y = 186

 

Solve the brackets.

 

150 - 5Y + 8Y = 186

 

150 + 3Y = 186 

 

Subtract 150 from both sides

 

3Y = 36 

 

Divide both sides by 3 

 

Y = 12.

 

There are 12 packages that weigh 8lbs.