Simultaneous equation word problem

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Discussion Overview

The discussion revolves around a word problem involving simultaneous equations related to purchasing textbooks within a budget. Participants explore how to formulate the equations based on the given conditions and seek guidance on solving them.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents the problem and formulates the first equation as 70x + 40y = 1440, expressing confusion about deriving a second equation.
  • Another participant confirms the first equation and suggests simplifying it by dividing through by 10, while also clarifying that the relationship between the quantities of the two volumes can be expressed as x = 2y.
  • A subsequent participant proposes the equation x = 2y as a potential second equation.
  • A later reply affirms the correctness of x = 2y and encourages substituting this equation into the first to solve for y, then using it to find x.

Areas of Agreement / Disagreement

Participants generally agree on the formulation of the equations, but the discussion remains focused on the process of solving them rather than reaching a final solution.

Contextual Notes

There is an assumption that the participants are familiar with the process of substitution in solving simultaneous equations, but specific steps beyond the formulation of equations are not detailed.

linapril
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"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.
 
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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?
 
Would x = 2y be right?
 
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.
 

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