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?

Answer 1

@phi

Answer 2

First, pick variable names for the unknowns.
can you do that ?

Answer 3

l for laser tag and v for video games

Answer 4

ok, but I would not use l because it looks like one (1) . how about L ?
also, be more clear: L and v are the COST of each type of game:

L= cost of laser tag games
v = cost of video games

next, look at this sentence:
Sam played 3 games of laser tag, 5 video games, and spent $17 total.

can you make an equation (showing cost of games plus cost of games = total cost) ?

Answer 5

if one laser tag game costs L dollars, how much does 3 games cost ?

Answer 6

3L?

Answer 7

yes. Sam played 3 games of laser tag, and it costs 3L
(he paid L dollars for each game... 3 times he dug into his pocket and paid for a laser tag game... paying L dollars each time: L+L+L or 3L dollars

Answer 8

Sam played 3 games of laser tag, 5 video games, and spent $17 total.

can you make an equation (showing cost of games plus cost of games = total cost) ?

Answer 9

if 1 video game costs v dollars, how much does 5 video games cost ?

Answer 10

5v. So would it be 3L+5v=17?

Answer 11

yes. you now have 1 equation and 2 unknowns

It is an important fact that you need as many equations as unknowns if you want to solve the system of equations.

you have 2 unknowns: L and v (cost of laser tag and cost of video)
you need one more equation.

use
Chris played 4 games of laser tag, 7 video games, and spent $23 total.

Answer 12

4L+7v=23

Answer 13

yes. now we are back in the land of algebra:

3L+5v=17
4L+7v=23

these are a bit ugly to solve but do-able. How would you solve them ?

Answer 14

are you going to use substitution or elimination ?

Answer 15

move 5v to the other side and substitute 17-5v for y in the second equation and solve for L

Answer 16

move 5v to the other side and substitute 17-5v for y

<grumble, grumble>

there is no "y". Remember, be *careful*

3L+5v=17
4L+7v=23

using the 1st equation, move 5v to the other side is right. you get:
3L = 17 - 5v

this says 3L is equal to 17 -5v
what is 1 L equal to? divide both sides by 3 to get 1L
3L/3 = (17-5v)/3 (notice we divide the whole side by 3... so we use parens)
L = (17-5v)/3

now substitute this in the 2nd equation. can you do this ?

Answer 17

which wad the 2nd equation?

Answer 18

3L+5v=17
4L+7v=23

Answer 19

solve for L in the first equation:
3L+5v=17

you get L = (17-5v)/3

substitute for L in the 2nd equation
4L+7v=23
what do you get ?

Answer 20

I got 15/13?

Answer 21

let's do it step by step. after substituting L = (17-5v)/3
into
4L+7v=23
what do you get ?

Answer 22

the idea is not think too hard (make each step simple)
so "erase" the L and put in (17-5v)/3
in
4L+7v=23

you get
\[ 4 \left( \frac{(17-5v)}{3} \right)+ 7v =23 \]

Answer 23

I don't like factions (I assume you don't either). One way to get rid of the 3 in the bottom is to multiply the equation (both sides, *all* terms) by 3
like this
\[ 4 \cdot 3 \left( \frac{(17-5v)}{3} \right)+ 3 \cdot 7v =23 \cdot 3 \]

Answer 24

the 3/3 "cancels" in the first term, so you get
\[ 4 \cdot \cancel{3} \cdot \frac{(17-5v)}{\cancel{3} }+ 3 \cdot 7v =23 \cdot 3\\
4 (17-5v) + 21v = 69

\]

Answer 25

solve for v

first, distribute the 4, then combine "like terms"