Sam and I have spent 2 days trying to solve this and have been unsuccessful. I’m trying NOT to look in the back for the answer and reverse engineer the solution.
Here’s a picture of our white board. It seems to me we’re very close but I’m stumped on how to guide him to the answer. Any suggestions from you gentle reader are greatly appreciated!
Whiteboard notes
Here’s the text of the problem, just in case:
Each pen cost $1.20 less than each notebook. Eric bought 8 pens and 2 notebooks. If he spent $21.90 altogether, how much did each notebook cost?
I always start off with what we know. Then we decide what we need to solve for-what is the answer going to be? In this problem, cost of the notebook so we will solve for N.
2N + 8P = 21.90
P = N – 1.80
Then just substitute the value of P into the top equation.
2N + 8 ( N – 1.80) = 21.90
This makes you only have one variable.
Then using distributive property-
2N + 8N -14.40 = 21.90
Then add your like variables
10N – 14.40 = 21.90
Then isolate your variable
10N = 21.90 -14.40
10N = 7.50
N = .75
The notebook costs 75 cents.
That is how we try to work through any algebra problem….same now even in high school. Decide what you know and what you need to figure out. Make a relationship using variables.
Hope that helps.
Barb-Harmony Art Mom
This is a basic 2 equations with 2 unknowns math problem.
You start with the two equations that you have
2N + 8P = 21.90
P = N -1.20
Then, you do substitution as Barb above stated. I am writing this out again for you, but the steps are the same as what Barb said, she just had a couple of numbers mixed up. Which is very easy to do in Math.
2N + 8(N-1.20) = 21.90
distributive Property results in.
2N + 8N -9.60 = 21.90
10N = 21.90 + 9.60 (Make sure to do the opposite of the operation on the other side of the equation)
10N = 31.50
N = 3.15
P= 3.15 – 1.20 = 1.95
I hope this is helpful.
Thank you Barbara and Lori! Your answers are very helpful. I pulled in a third (non algebra) explanation from another friend since we’re not at this stage yet. BUT we could both see how the algebraic answers mirrored what we did. Cool!