Question

Bill bought 4 pens for $12. Which of the following equations shows the relationship between the cost of pens, c, and the number of pens, x, bought? What will the cost of 20 pens be?

options:

c = 3x, $12

x = 3c, $60

c = 3x, $60

x = 3c, $12

Answer 1

The answer to your question is: c = 3x, $60

Explanation:

Bill bought = 4 pens for $12

equation cost vs # of pens (x)

Cost of 20 pens?

4 pens ---------------- $12

1 pen ------------- x

x = 1(12)/4

x = 3

Equation :

cost = 3x

20 pens will cost

cost = 3(20)

= $60

Answer : c = 3x, $60

Answer 2

The correct option is

`c=3x` , $60

Explanation:

We start by assuming that exists a linear relationship between the price of the pens and the amount of pens that Bill bought.We also assume that this linear relationship is a direct linear relationship.This means that the price of the pens increases with the amount of pens. According to this we can calculate the price of one pen as :

`(4)/(12)=(1)/(x)`

Solving for ''x'' :

`(4)/(12)=(1)/(x) \\x=((12).(1))/(4)=3`

We find that one pen costs $3

If ''c'' is the cost of pens and ''x'' is the number of pens we can write the ''cost function'' multiplying the cost per pen by the amount of pens :

cost = (cost per pen).(amount of pens) ⇒

`c=3x`

Because cost is the letter ''c'' and the amount of pens is represented by the variable ''x''

To know the cost of 20 pens we only need to replace in the cost function ''c'' the variable ''x'' by 20 ⇒

`c=3x\\c=(3).(20)=60\\c=60`

Finally, the cost function is

`c=3x`

And the cost of 20 pens is $60. Therefore, the third option is the correct option.