Can you please explain to me how to do the work for this?

Marcella and Danilo went to a bookstore. Marcella bought 2 notebooks and 3 pens for $14.50. Danilo bought 1 notebook and 2 pens for $7.50. How much does 1 notebook cost?





i have the answer for this, it's:





$6.50





but i still don't get how to do the work -.- can you help me?Can you please explain to me how to do the work for this?
Let N = Notebook Let P = Pen





2N + 3P = 14.50


1N + 2P = 7.50





1N +2P - 2P = 7.50 - 2P


1N = 7.50 - 2P


Substitute into the first equation for N


2N + 3P = 14.50


2(7.50 - 2P) + 3P = 14.50


15.00 - 4P + 3P = 14.50


15.00 - P = 14.50


15.00 - P - 15.00 = 14.50 - 15.00


- P = - .50


P = .50


Substitute into the second equation


1N + 2P = 7.50


1N + 2(.50) = 7.50


1N + 1.00 = 7.50


1N + 1.00 - 1.00 = 7.50 - 1.00


1N = 6.50Can you please explain to me how to do the work for this?
okay first of all you need to set your equations and define your variables


soo let n represent the number of notebooks and p represent the number of pens.


okay than you read the question carefully


';Marcella bought 2 notebooks and 3 pens for $14.50'; that means that she bought 2 and added 3 pens. soo your first equation would be y=2n +3p=14.50 (total cost)


and than ';danilo bought 1 notebook and 2 pens for $7.50'; soo your second equation would look like y=n+2p=7.40


than you solve by substitution


sub second equation into the first


2(-2p+7.50)+3p=14.50---%26gt;use distributive property


-4p + 15+3p=14.50--%26gt; collect like terms ; bring 15 to other side and add the p's


-p=14.50-15--%26gt; simplify


-p=-0.5--%26gt; divide both sides by negative one to isolate the negative


p=0.5


than you sub p into the second equation to find the number of notebooks


n=-2(0.5)+7.50


n=-1 +7.50


n=6.50


Therefore, one notebook costs $6.50
Let x = cost per notebook


Let y = cost per pen





2x + 3y = 14.50 Marcella's purchase


x + 2y = 7.50 Danilo's purchase





Solve the second equation for x





x + 2y = 7.50


x = 7.50 - 2y





Sub this into the first equation





2(7.50 - 2y) + 3y = 14.50


15 - 4y + 3y = 14.50


-y = -.50


y = .50





Sub this value in for y in the second equation





x + 2(.50) = 7.50


x + 1 = 7.50


x = 6.50, the cost for one notebook.
This is a simultaneous equation problem.


Marcella's purchase: 2n + 3p = 14.50


Danilo's purchase: n + 2p = $7.50





There are two methods, the easiest here is:


Use Danilo's to solve for n and substitute in Marcella's equation:


n=7.50-2p then... 2(7.50-2p)+3p=14.50;


simplify to 15.00 - 4p +3p = 14.50 p=.50


n=6.50
What i like doing is graphing a line for each equation


2x +3y=14.50


1x +2y=7.50


where they intercect is the prices


the point (6.5, 0.5)


that means a notebook is $6.50


and a pancil is $0.50
x = notebook


y = pen





2x+3y=1450


[x+2y=750]-2





-y=-50


y=50





x+2(50)=750


x+100=750


x=650





$.50 per pen


$6.50 per notebook