Sam and Chris went to “Lots O Fun” to play laser tag and video games for Chris’s birthday. Sam played 3 games of laser tag, 5 video games, and spent $17 total. Chris played 4 games of laser tag, 7 video games, and spent $23 total. How much does one video game cost to play?
a. $1
b. $2
c. $3
d. $4

Question

Sam and Chris went to “Lots O Fun” to play laser tag and video games for Chris’s birthday. Sam played 3 games of laser tag, 5 video games, and spent $17 total. Chris played 4 games of laser tag, 7 video games, and spent $23 total. How much does one video game cost to play? 
a. $1 
b. $2 
c. $3 
d. $4

anonymous · Answer

sam: 3 games of laser,
 5 video games,
 spent - $17
 
chris: 4 games of laser,
 7 video games,
 spent - $23
 
turn this into an equation. Lets call the 'laser games' x, and the 'video games' y.
 
so, for sam: 3x + 5y = 17
 
and for chris: 4x + 7y = 23
 
but we want to know how much a single video game costs. This is where simultaneous equations come in.
 
we only want the y's left in the equation, seeing as these stand for the 'video games' and that's what we're trying to find. So we need to get rid of the x's. To do this, we subtract one equation away from the other. But there's a problem - we have 4 x's in one, and 3 x's in the other, so at this stage if we subtracted one equation away from the other we'd still have an x left in there - and we want none left in the equation.
 
So we need to multiply each equation so that we have the same amount of x's in both. The lowest common multiple that 3 and 4 will both go into is 12. So at the moment we have:
 
3x + 5y = 17 and
 4x + 7y = 23
 
we're going to change this so that:
 
12x + 20y = 68 and
 12x + 21y = 69
 
unfortunately, you can't just stick in some 12x's to cancel each other out without changing the rest of the equation. Whatever you do to one value you have to do to the rest of the equation.
 (3 x 4 = 12, 5 x 4 = 20, 17 x 4 = 68) Here you have to multiply every value by 4
 
and (4 x 3 = 12, 7 x 3 = 21, 23 x 3 = 69) and here you have to multiply every value by 3
 

Now we will just be left with y's when we subtract one equation away from the other. Yay!
 
So:
 12x + 20y = 68 < take this equation away from
 12x + 21y = 69 < this one
 
12 - 12 = 0 x's
 21 - 20 = 1 y
 69 - 68 = 1
 
so y = 1
 therefore y = $1, so one video game costs $1.

anonymous · Answer

1 dollar

anonymous · Answer

you copied all that from YahooAnswers..

parthkohli · Answer

Assume that laser tag is $l$ and video games is $v$. We have two simultaneous equations:$$ 3l + 5v = 17 \ 4l + 7v = 23$$Solve for $v$.

anonymous · Answer

no i typed that on yahoo hayley is my sister