# 1 pencil, 1 pen cost $8; 2 pencils, 3 pens cost$21; find cost of pencil, pen

#### 400396

##### New member
hello all.
I have a problem with this question:

1 pencil and 1 pen cost $8 together. 2 pencils and 3 pens cost$21 together.
What the cost of 1 pencil and 1 pen?

I know that the answer is $3 for a pencil and$5 for a pen, but i don't know what equation to use.

I appreciate any help on this.
thanks.

#### stapel

##### Super Moderator
Staff member
1 pencil and 1 pen cost $8 together. 2 pencils and 3 pens cost$21 together.
What the cost of 1 pencil and 1 pen?

I know that the answer is $3 for a pencil and$5 for a pen, but i don't know what equation to use.
Since you posted this to "Pre-Algebra" and haven't even picked any variables, I'll assume that you don't know about variables and other algebraic stuff. So let's use plain arithmetic.

i. You are given the cost of one pencil and one pen. What then will be the cost of two pencils and two pens? (Hint: Multiply.)

ii. You are given the cost of two pencils and three pens, and you just found the cost of two pencils and two pens. What then is the cost of one pen? (Hint: Subtract.)

iii. You are given the cost of one pencil and one pen. You just found the cost of one pen. What then is the cost of one pencil? (Hint: Subtract.)

#### melis

##### New member
If you have worked with variables, you can let x=#of pencils and y=#of pens and write two equations using the information.
The first equation would be x+y=8 and the second would be 2x+3y=21 and now you have a system of equations to solve.

#### mmm4444bot

##### Super Moderator
Staff member
… i don't know what equation to use …
You haven't followed our basic forum guidelines, so I can't guess whether you may have been taught about systems of equations. Here's an alternate approach, using a single variable.

x = pencil price

We're told that one pencil plus one pen costs $8. Therefore: 8 - x = pen price The cost to purchase 2 pencils and 3 pens is given as$21. Use this information, to form your equation. In other words:

2(pencil price) + 3(pen price) = 21