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

Answer 1

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

Step-by-step explanation:

Let x be the cost of a one pack of ballpoint pens and y be the cost of one pack of gel pens.

Then by considering the given description in question , we have the following system of equations:-

$60x+25y=355----------(1)\\\\ 120x+30y=570--------(2)$

Multiply equation (1) by 2 on both the sides , we get

$120x+50y=710---------(3)$

Eliminate equation (2) from (3) , we get

$20y=140\\\\ y=\dfrac{140}{20}=7$

Put y= 7 in (1), we get

$60x+25(7)=355\\\\ 60x+175=355\\\\ 60x=355-175=180\\\\ x=\dfrac{180}{60}=3$

Hence, the cost of a one pack of ballpoint pens is $3 and the cost of one pack of gel pens is $7.

Answer 2

Answer:

$3 for ballpoint pens and $7 for gel pens.

Step-by-step explanation:

Let b represent the cost for ballpoint pens and g represent the cost for gel pens.

For the first equation, we have

60b+25g = 355

For the second equation, we have

120b+30g = 570

This gives us the system

$\left \{ {{60b+25g=355} \atop {120b+30g=570}} \right.$

To solve this, we will use elimination.  We will first make the coefficients of b the same by multiplying the top equation by 2:

$\left \{ {{2(60b+25g=355)} \atop {120b+30g=570}} \right. \\\\\left \{ {{120b+50g=710} \atop {120b+30g=570}} \right.$

Next we will subtract the bottom equation from the top:

$\left \{ {{120b+50g=710} \atop {-(120b+30g=570)}} \right. \\\\20g=140$

Divide both sides by 20:

20g/20 = 140/20

g = 7

The gel pens cost $7.

Substitute this in place of g in the first equation:

60b+25(7) = 355

60b+175 = 355

Subtract 175 from each side:

60b+175-175 = 355-175

60b = 180

Subtract 60 from each side:

60b/60 = 180/60

b = 3

The ballpoint pens cost $3.