Question

an office supply company orders packs of pens for two of its stores. for the first store, the order is for 60 packs of ballpoint pens and 25 packs of gel pens, for a total of \\$355. for the second store, the order is for 120 packs of ballpoint pens and 30 packs of gel pens, for a total of \\$570.

create and solve a system of equations to determine the cost of one pack of ballpoint pens and one pack of gel pens.

• the cost of one pack of ballpoint pens is \\$3 and the cost of one pack of gel pens is \\$7.
• the cost of one pack of ballpoint pens is \\$4 and the cost of one pack of gel pens is \\$3.
• the cost of one pack of ballpoint pens is \\$3 and the cost of one pack of gel pens is \\$4.
• the cost of one pack of ballpoint pens is \\$7 and the cost of one pack of gel pens is \\$3.

Explanation:

⚡ Using what you learned: Solving Systems by Elimination (Addition)

Step 1: Define variables and set up the system

Let \( b \) be the cost of one pack of ballpoint pens and \( g \) be the cost of one pack of gel pens.

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$$

Step 2: Solve by elimination

Multiply the first equation by \(-2\) to eliminate \( b \):

$$ -120b - 50g = -710 $$

Add this to the second equation:

$$ (-120b - 50g) + (120b + 30g) = -710 + 570 $$

$$ -20g = -140 $$

$$ g = 7 $$

Step 3: Solve for the remaining variable

Substitute \( g = 7 \) back into the first equation:

$$ 60b + 25(7) = 355 $$

$$ 60b + 175 = 355 $$

$$ 60b = 180 $$

$$ b = 3 $$

Answer:

The cost of one pack of ballpoint pens is $3 and the cost of one pack of gel pens is $7.