Simultaneous equation word problem

[linapril]

"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]

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]

Would x = 2y be right?

 

[MarkFL]

That would be exactly right!

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.

 

[CellCoree]

To solve this simultaneous equation word problem, we can use the information given and set up two equations:

Let x = number of copies of Maths for All volume 1
Let y = number of copies of Maths for All volume 2

From the given information, we know that the total budget is 1440 euros, so our first equation is:

70x + 40y = 1440

We also know that the department wants twice as many copies of volume 1 as volume 2, so our second equation is:

x = 2y

Now we have two equations and two unknowns, so we can solve for x and y by substituting the value of x from the second equation into the first equation:

70(2y) + 40y = 1440
140y + 40y = 1440
180y = 1440
y = 8

Now we can plug this value back into our second equation to solve for x:

x = 2(8)
x = 16

Therefore, the department can buy 16 copies of Maths for All volume 1 and 8 copies of Maths for All volume 2 with their budget of 1440 euros.