How many boxes of tennis balls were sold?

Question

Each box of tennis balls contains 3 tennis balls, while each box of baseballs only contains 2 baseballs. A sporting-goods store sold 26 boxes of tennis balls and baseballs. If a total of 70 balls were sold,  how many boxes of tennis balls were sold? 

Answer 1

For this problem, we are going to sort the quantities into two different equations. An equation for the number of boxes and an equation for the total number of balls.

 

Each box of tennis balls (t) has three balls (3). Each box of baseballs (b) has two balls (2). There were 70 balls sold.

 

3t + 2b = 70

 

We don't know how many of each type of box were sold but we do know 26 boxes total were sold. Using the same variables from above, we can write an equation for the number of boxes.

 

t + b = 26

 

To solve our problem, we are going to solve for t in the second equation.

So we get t = 26 - b.

 

Now we can plug t=(26-b) into our first equation.

The original:                                                  3t + 2b = 70

Plug in the value for t:                            3(26-b) + 2b = 70

Now distribute the 3:                               78 - 3b +2b = 70

Now subtract 70 from both sides and combine like terms:  8 - b = 0

We can't leave our equation equal to zero so move b to the opposite side: 8 = b

Now that we know b = 8, or there were 8 boxes of baseballs sold, we can put b back into our original equation for the total number of boxes.

Original: t + b = 26

Plug in b value: t + 8 = 26

Solve: t = 18

 

18 boxes of tennis balls were sold.