Question

1. the cost of 3 boxes of envelopes and 4 boxes of notebook paper is $13.25. two boxes of envelopes and 6 boxes of notebook paper cost $17. find the cost of each.

Explanation:

Step1: Define Variables

Let \( x \) be the cost of one box of envelopes (in dollars) and \( y \) be the cost of one box of notebook paper (in dollars).

Step2: Set Up Equations

From the problem, we have two equations:

1. \( 3x + 4y = 13.25 \) (cost of 3 envelopes and 4 notebook papers)
2. \( 2x + 6y = 17 \) (cost of 2 envelopes and 6 notebook papers)

Step3: Solve the System of Equations

First, we can simplify the second equation by dividing by 2: \( x + 3y = 8.5 \), so \( x = 8.5 - 3y \).
Now substitute \( x = 8.5 - 3y \) into the first equation:

$$
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$$

Now substitute \( y = 2.45 \) back into \( x = 8.5 - 3y \):

$$
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$$

Answer:

The cost of one box of envelopes is \(\$1.15\) and the cost of one box of notebook paper is \(\$2.45\).