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(52810)  (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.
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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.
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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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