The total cost of 3 notepads and 1 pen is twice the total cost of 1 notepad and 3 pens. The total cost of 4 notepads and 1 pen is how many times the total cost of 1 notepad and 4 pens?
Question
The total cost of 3 notepads and 1 pen is twice the total cost of 1 notepad and 3 pens. The total cost of 4 notepads and 1 pen is how many times the total cost of 1 notepad and 4 pens?
Solution
Let's denote the cost of a notepad as N and the cost of a pen as P.
From the first sentence, we have the equation: 3N + P = 2(N + 3P), which simplifies to 3N + P = 2N + 6P. If we rearrange this, we get N = 5P.
Now, we want to find out how many times the total cost of 4 notepads and 1 pen is compared to the total cost of 1 notepad and 4 pens.
So, we need to find the ratio of (4N + P) to (N + 4P).
Substituting N = 5P into these expressions, we get:
(4*5P + P) / (5P + 4P) = (20P + P) / (5P + 4P) = 21P / 9P = 21/9 = 7/3.
So, the total cost of 4 notepads and 1 pen is 7/3 times the total cost of 1 notepad and 4 pens.
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