SOLUTION: Miguel and Javier went to an arcade where the machines took tokens. Miguel played 9 games of ping pong and 5 games of pinball, using a total of 29 tokens. At the same time, Javie

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Question 1189810: Miguel and Javier went to an arcade where the machines took tokens. Miguel played 9 games of ping pong and 5 games of pinball, using a total of 29 tokens. At the same time, Javier played 3 games of ping pong and 1 game of pinball, using up 7 tokens.
Part A: Write a system of equation to model this situation

Found 3 solutions by ankor@dixie-net.com, Theo, ikleyn:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Miguel and Javier went to an arcade where the machines took tokens.
Miguel played 9 games of ping pong and 5 games of pinball, using a total of 29 tokens.
At the same time, Javier played 3 games of ping pong and 1 game of pinball, using up 7 tokens.
Part A: Write a system of equation to model this situation
;
let a = no. of tokens for each ping pong game
let b = no. of tokens for each pinball game
:
An equation for each player
9a + 5b = 29
3a + 1b = 7

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
x = price of a ping pong token.
y = price of a pinball token.

9x + 5y = 29
3x + y = 7

multiply both sides of the second equation by 3 and lave the first equation as is to get:

9x + 5y = 29
9x + 3y = 21

subtract the second equation from the first to get:

2y = 8

solve for y to get y = 4
use y = 4 to solve for x to get x = 1

replace x and y with 4 and 1 in the original equations to get:
9x + 5y = 29 becomes 9 + 20 = 29
3x + y = becomes 3 + 4 = 7
this confirms the values are good.

you were asked to write a system of equation to model the situation.
that solution is:

9x + 5y = 29
3x + y = 7
x = price of a ping pong token.
y = price of a pinball token.

i went a little further and solved it, but that's not what they asked.

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Miguel and Javier went to an arcade where the machines took tokens.
Miguel played 9 games of ping pong and 5 games of pinball, using a total of 29 tokens.
At the same time, Javier played 3 games of ping pong and 1 game of pinball, using up 7 tokens.
Part A: Write a system of equation to model this situation.
~~~~~~~~~~~~~~

Let x be the number of tokens to play ping pong,

    y be the number of tokens to play pinball.


Then the system of equation is as you read the problem

    9x + 5y = 29   tokens  (as Miguel played)

    3x +  y =  7   tockens (as Javier played).

Solved and completed.

---------------

For many similar problems,  writing systems of equations  (setup)  is usually quite simple routine part of the solution.

The key words in this activity,  that may help to a beginner student,  are  "write equations as you read the problem".

These words define an instruction for you "what to do" :  read the problem first and then re-read it
as many times as you need to get full understanding of the condition and understanding on what to do.

To extend your practice/knowledge,  see the lessons
    - Roses and violets
    - Counting calories and grams of fat in combined food
    - A theater group made appearances in two cities
    - Exchange problems solved using systems of linear equations
    - Typical word problems on systems of 2 equations in 2 unknowns
    - HOW TO algebreze and solve this problem on 2 equations in 2 unknowns
in this site.


After reading these lessons,  you will tackle such problems without asking for help from outside.


///////////////


The lesson to learn from my post is THIS :

        The internal combustion engine needs to turn on the ignition first to start working.

        Likewise, begin your work on solving word problems saying  " write equation/equations as you read the problem ".



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