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Simultaneous equation word problem

linapril

New member
Dec 21, 2012
23
"A school mathematics department has 1440 euros to buy textbooks.
Maths for All volume 1 costs 70 euros. Maths for All volume 2 costs 40 euros.
The department wants twice as many copies of volume 1 as volume 2.
How many of each volume can they buy?"

I got up to that the first equation is 70x + 40y= 1440, but I have no idea how to proceed after that. How do I get a constant in the second equation? I'm lost.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
You have chosen to let x represent the number of vol. 1 and y represents the number of vol. 2 purchased.

Your first equation is good, although I would divide through by 10 so the numbers are smaller. Now, we are also told:

"The department wants twice as many copies of volume 1 as volume 2."

This means x must be twice the value of y. How can you write this mathematically?
 

linapril

New member
Dec 21, 2012
23
Would x = 2y be right?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
That would be exactly right!:cool:

So, we now have:

$\displaystyle 7x+4y=144$

$\displaystyle x=2y$

Now, use the second equation, and substitute for x into the first equation to get an equation in y, which you can then solve. Once you have the value of y, then use the second equation to get x.