SOLUTION: Solve using substitution method For 2000 dollars are bought 15 notebooks and 12 markers. How much does 1 notebook and much does 1 marker cost, if 3 markers cost as much as 6 noteb

Question 1095807: Solve using substitution method
For 2000 dollars are bought 15 notebooks and 12 markers. How much does 1 notebook and much does 1 marker cost, if 3 markers cost as much as 6 notebooks?
solving looks something like
12x+15y=2000
6y=3x
Please explain thoroughly and step by step :)
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you buy 15 notebooks and 12 markers for 2000.

how much does 1 notebook and 1 marker cost, if 3 markers cost as much as 6 notebooks.

let x equal the price of a notebook.
let y equal the price of a marker.

15x + 12y = 2000

this equation says that 15 times the price of a notebook plus 12 times the price of a marker is equal to 2000 dollars.

3 markers cost as much as 6 notebooks.

3y = 6x

this equation says that 3 times the price of a marker is equal to 6 times the price of a notebook.

you have two equations that need to be solved simultaneously.

they are:

15x + 12y = 2000
3y = 6x

when you solve by substitution, you solve for one of the variables in one of the equations and then use that value in the other equationm.

either equation will do.

i'll use the first equation to solve for y.

start with 15x + 12y = 2000
subtract 15x from both sides of the equation to get 12y = 2000 - 15x
divide both sides of the equation by 15 to get y = (2000 - 15x) / 12

use that value for y in the second equation.

start with 3y = 6x
replace y to get 3 * (2000 - 15x) / 12 = 6x.
divide both sides of the equation by 3 to get (2000 - 15x) / 12 = 2x.
multiply both sides of the equation by 12 to get 2000 - 15x = 24x.
add 15x to both sides of the equation to get 2000 = 39x.
divide both sides of the equation by 39 to get 2000 / 39 = x.
solve for x to get x = 2000 / 39 = 51.28205128.

go back to the original equation of 15x + 12y = 2000 and replace x with the value that you calculated for it.

you will get 15 * 51.28205128 + 12y = 2000
solve for y to get y = (2000 - 15 * 51.28205128) / 12.
result is y = 102.5641026

go back to both original equaitons and see if they're true when you replace x and y with their calculated values.

3y = 6x becomes 3*102.5641026 = 6*51.28205128
result is 3076923077 = 307.6923077 which confirms this equation is good.

15x + 12y = 2000 becomes 15*51.28205128 + 12*102.5641026.
result is 2000 = 200 which confirms this equation is also good.

you probably want to round your numbers to the nearest penny.

therefore, your solution should be:

x = 51.28
y = 202.56

if you try to confirm with these rounded numbers, you won't be exactly right because of the rounding.

you need to use the un-rounded numbers for your confirmation.

note that i had:

15x + 12y = 2000
3y = 6x

and you had:

12x+15y=2000
6y=3x

it looks to me like i was using x as the price of a notebook and you were using x as the price of a marker.

replace your x with y and you y with x and we're the same.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Solve using substitution method
For 2000 dollars are bought 15 notebooks and 12 markers. How much does 1 notebook and much does 1 marker cost, if 3 markers cost as much as 6 notebooks?
solving looks something like
12x+15y=2000
6y=3x
Please explain thoroughly and step by step :)

This is very simple! Let the price of a notebook be N, and that of a marker, M Then we get: 15N + 12M = 2,000 ------- eq (i) Also, ------ eq (ii) 15N + 12(2N) = 2,000 ------ Substituting 2N for M in eq (i) 15N + 24N = 2,000 39N = 2,000 N, or cost of a notebook = Just multiply the cost of 1 notebook by 2 to get the cost of 1 marker. That's all!! Nothing COMPLEX and/or CONFUSING.

RELATED QUESTIONS
Solve using substitution method For 2000 dollars are bought 15 notebooks and 12 markers. (answered by josmiceli)
Michael bought 2 notebooks and 1 pen for 7$. Rick bought 1 notebook and 5 pens for 8$.... (answered by Cromlix)
Need help with setting up equation for...Mary bought 2 notebooks and 3 pens for $14.50.... (answered by stanbon,Alan3354)
Three�of�Carlos��and�Amy's�friends�are�purchasing�school�supplies�at�the�bookstore.Stan�bu (answered by rothauserc)
Marty recently bought 6 notebooks, 5 pens, and 4 markers. A notebook costs 5 cents less... (answered by ptaylor)
Five notebooks and a pack of pencils costs $7. Two notebooks and 2 packs of pencils cost... (answered by math_helper)
A store is selling 100 notebooks. 36 yellow notebooks, 42 blue notebooks and 22 red... (answered by ewatrrr,ikleyn)
$8.75 for 3 notebooks and 5 pens, how many dollars are the notebooks (answered by greenestamps)
maria purchased 12 pens and 8 notebooks for $15.00. bob bought 4 pens and 3 notebooks for (answered by checkley75)