Question 1095807
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.