Brian D. answered • 12/20/19
Experienced Tutor Specializing in Science, Math, and Chess
This is a question for simultaneous equations. We have to figure out the cost of a movie and the cost of a video game.
I will use the variable "m" for the cost of a single movie and the variable "v" for the cost of a single video game.
Equation A:
12 movies and 2 video games cost $41 so we have the equation:
12m + 2v = 41
Equation B:
3 movies and 5 video games cost $35 so we have the equation:
3m + 5v = 35
To reiterate, we have these two equations:
A) 12m + 2v = 41
B) 3m + 5v = 35
Now, we have to get rid of one of the variables since you cannot solve an equation that has more than one variable. It is your choice which variable you choose to get rid of. I will get rid of the "m." Since I am getting rid of the "m" in the equation I need to make the coefficient (the number in front of the variable the same).
Equation A has a "12" in front of the "m" and Equation B has a "3" in front of the "m." Since 3 is a factor of 12 we can multiply equation B by 4 (since 3 * 4 = 12).
B*4) 4(3m + 5v = 35) = 12m + 20v = 140
We can line the equations up and then subtract them:
A) 12m + 2v = 41
-
B4) 12m + 20v = 140_______
0m -18v = -99
So, now we have the simplified equation of:
-18v = -99 Dividing both sides by -18 (to get the "v" alone) gives us:
v = 5.50 (remember since the question is about cost we need two decimal places for the "cents."
We just figured out that the cost of one video game is $5.50 . Now, we have to take one of the original equations (it doesn't matter which one, and plug in 5.50 for "v." After that, we will solve for "m"). I have chosen to use equation A.
12m + 2v = 41
12m + 2(5.50) = 41
12m + 11 = 41
12m = 30
m = 2.50
We just figured out that the cost of one movie is $2.50
