Question
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 one 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 ?
Hint:
1. Total bottles in the refrigerator = Original number of bottles + Bottles in full box + Bottles in box with 1 less than full box
2. Bottles in full boxes = number of full boxes * bottles per full box
3. Bottles in boxes with 1 less than full box = number of boxes × bottles per box
The correct answer is: Number of bottles in a full box is 12
Step-by-step solution:-
Let the number of bottles in a full box be x.
Original number of bottles = 9 ...................................... (From given information) ................... (Equation i)
Now, Bottles in a full boxes = number of full boxes × bottles per full box
∴ Bottles in a full boxes = 3 * x …............................ (From given information) …................ (Equation ii)
Bottles in a box with 1 less bottle than a full box = number of boxes × bottles per box
∴ Bottles in a box with 1 less bottle than a full box = 2 × (x-1)
∴ Bottles in a box with 1 less bottle than a full box = 2x - 2 ...................................................... (Equation iii)
We know that-
Total bottles in the refrigerator = Original number of bottles + Bottles in full box + Bottles in box with 1 less than full box
∴ 67 = 9 + 3x + (2x-2) .................................................................... (From given information & Equations i, ii & iii)
∴ 67 = 9 + 3x + 2x - 2
∴ 67 - 9 + 2 = 3x + 2x ........................................................ (Taking all the constants together)
∴ 60 = 5x
∴ 60/5 = x
∴ 12 = x
Final Answer:-
∴ Number of bottles in a full box is 12.
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