Question

e There are nine water bottles in Devin’s refrigerator. He adds three full boxes of water bottles to the refrigerator. Then he adds two more boxes that each have 1 fewer bottle than a full box. When he is done, there are 67 bottles in the refrigerator. Write and solve an equation to find the number of bottles in a full box

Answer 1

To solve this problem, we can write an equation letting the variable x represent the number of bottles in a box of water (this means that the expression x-1 represents the boxes that have one fewer bottle than a full box).

This allows us to create the following equation:

9 original bottles + 3x (3 full boxes) + 2(x-1) (two boxes with one fewer bottle) = 67 total bottles

OR

9 + 3x + 2(x-1) = 67

Now, we can begin to solve this equation by using the distributive property to get rid of the parentheses on the left side of the equation.

9 + 3x + 2x - 2 = 67

Next, we can combine like terms on the left side of the equation (meaning add the variable terms together and subtract the constant terms).

7 + 5x = 67

Now, we should subtract 7 from both sides of the equation to get the variable term alone on the left side of the equation.

5x = 60

Next, we should divide both sides by 5 to isolate the variable x on the left side of the equation.

x = 12

Therefore, your answer is that there are 12 bottles in a full box.

Hope this helps!