Respuesta :
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
[tex]\left \{ {{60b+25g=355} \atop {120b+30g=570}} \right.[/tex]
To solve this, we will use elimination. We will first make the coefficients of b the same by multiplying the top equation by 2:
[tex]\left \{ {{2(60b+25g=355)} \atop {120b+30g=570}} \right. \\\\\left \{ {{120b+50g=710} \atop {120b+30g=570}} \right.[/tex]
Next we will subtract the bottom equation from the top:
[tex]\left \{ {{120b+50g=710} \atop {-(120b+30g=570)}} \right. \\\\20g=140[/tex]
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.
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:-
[tex]60x+25y=355----------(1)\\\\ 120x+30y=570--------(2)[/tex]
Multiply equation (1) by 2 on both the sides , we get
[tex]120x+50y=710---------(3)[/tex]
Eliminate equation (2) from (3) , we get
[tex]20y=140\\\\ y=\dfrac{140}{20}=7[/tex]
Put y= 7 in (1), we get
[tex]60x+25(7)=355\\\\ 60x+175=355\\\\ 60x=355-175=180\\\\ x=\dfrac{180}{60}=3[/tex]
Hence, the cost of a one pack of ballpoint pens is $3 and the cost of one pack of gel pens is $7.
