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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?

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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.

This problem has been solved

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