if 1 notebook= 4 pencils, 1 pencil+1 notebook = 28?

Question

if 1 notebook= 4 pencils, 1 pencil+1 notebook = 28?

how much is each pencil worth and how much is the notebook worth

Answer 1

Hello!

Your profile says Algebra 1, so I assume the best way for you to solve this problem is to create a system of equations. Then, solve the system using substitution.

1. Define your variable: Let n = notebook and p = pencil.
2. Write two equations based off of the information given in the word problem (this is usually the trickiest part for most students):
3. The first sentence translates to the equation n = 4p.
4. The second sentence translates to p + n = $28
5. Because the first equation is already solved for one variable (n), substitution is the 'easiest' method for solving this system. Everywhere you see the variable n in the second equation, you will plug in '4p' instead.

n = 4p, SO.....

p + n = $28

p + 4p = $28 (Now solve the equation)

5p = $28 (combine like terms)

p = $28/5 (divide by 5 on both sides)

p = $5.60

If p = $5.60, we can now solve for n.

n = 4p

n = 4(5.60)

n = $22.40

THE PENCIL COSTS $5.60 AND THE NOTEBOOK COSTS $22.40.

Let me know if you need further explanation. A lot of basic skills are required to solve this problem (substitution, solving equation, fractions, decimals, etc). If you let me know specifically which part causes trouble, we can work from there.