Ethere 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

We want to create and solve an algebraic equation that says the number of water bottles in a full box.

The information we have is:

Originally, there are 9 bottles in the refrigerator.

Then he adds 3 full boxes, if each box has N bottles, then he added 3N bottles.

Then he adds 2 boxes with 1 fewer bottle than a full box, then he added 2(N - 1) bottles.

Finally, there are 67 bottles in the refrigerator.

Then, adding all the bottles that he originally had in the refrigerator and the ones he added later, we have:

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

Now we can solve this for N

9 + 3N + 2N - 2 = 67

5N + 7 = 67

5N = 67 - 7 = 60

N = 60/5 = 12

N = 12

From this, we can conclude that each full box has 12 bottles.

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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!

answer: 7270

step-by-step explanation:

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2