1 pen cost $0.40 less than 3 pencils. Anthony paid $5.80 for 2 pens and 5 pencils. Whats the cost 0f 1 pencil.

Answer 1

If one pen costs .40 less than 3 pencils

Let x= Pens, y= Pencils

then x= 3y -.40

We can write a second equation based on the sentence, "Anthony paid $5.80 for 2 pens and 5 pencils" :

5.80= 2x + 5y

Next, use substitution and rewrite the second equation, using the first in place of "x" :

5.80= 2(3y-.40) + 5y

Now that there is only one variable, this is possible to solve.

5.80=6y-.80+5y

5.80=11y-.80

6.60=11y

y=0.60

So one pencil is $0.60

Answer 2

To solve this problem, we need to pick variables that can represent the cost of a pen and the cost of a pencil, put them in terms of each other and solve for the values.

I have chosen the following variables

p=the cost of a pen

AND

x= the cost of a pencil

The problem informs us that 1 pen costs $.40 less than 3 pencils. We can write this as an equation:

p=3x-.4

Then the question also tells us that the total cost of 2 pens and 5 pencils is $5.80. We can write this as an equation: 2p+5x=5.8.

Traditionally, we cannot solve an equation when we have more than one unknown value, so in this situation, we can substitute the value 3x-.4 for p, which gives us:

2(3x-.4)+5x=5.8

Distribute the 2.

6x-.8+5x=5.8

Combine like terms.

11x-.8=5.8

11x=6.6

Divide by 11 to solve for x.

x=.6

The cost of one pencil is $.60.