Question
A cereal box manufacturer changes the size of the box to increase the amount of cereal it contains . The equations 12 + 7.6n and 6 + 8n , where n is the number of smaller boxes, are both representative of the amount of cereal that the new larger box contains . How many smaller boxes equal the same amount of cereal in the larger box ?
Hint:
The manufacturer has started producing 2 new sizes of cereal box that has a specific relation to the size of earlier used smaller boxes.
We need to find the number of smaller boxes i.e. value of n for which the quantity in both the larger boxes is the same.
The correct answer is: The quantity of cereal in both the larger boxes will be same for 15 smaller boxes.
Step-by-step solution:-
As per the information given in the question, we get-
Let the 2 new boxes category be b1 & b2.
The relation between size of b1 & smaller boxes can be represented by the equation 12 + 7.6n
The relation between size of b2 & smaller boxes can be represented by the equation 6 + 8n
Now, we need to find the value of n for which the quantity of cereal in larger boxes b1 & b2 are the same.
∴ equating both the equations we get-
12 + 7.6n = 6 + 8n
∴ 12 - 6 = 8n - 7.6n
∴ 6 = 0.4n
∴
= n
∴ 15 = n
Final Answer:-
∴ The quantity of cereal in both the larger boxes will be same for 15 smaller boxes.
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