Question

One month Miguel rented



5
movies and



3
video games for a total of



$

27
. The next month he rented



2
movies and



12
video games for a total of



$

81
. Find the rental cost for each movie and each video game.

Answer 1

@lall

Answer 2

since both the costs are not dependent on each other.
ther is no interrelation b/w both the costs in the given question.
so you have to take two variables say x & y for both the costs.

Answer 3

let the rent of one movie= x
let the rent of one video games=y
ATQ
5x + 3y= 12 ...............equation 1
2x + 12y= 81...............equation 2

Answer 4

now there are different ways to solve 2 simultaneous equation like elimination, cross multiplication, substitution.
i am using elimination method now.

Answer 5

in the elimination method u hav to eliminate one variable out of 2 to get the value of one variable and then substituting the value in one of the 2 equations to get the value of another variable

Answer 6

so solving equations (1) & (2)
multiply equation(1) by 2
multiply equation (2) by 5

Answer 7

you get
[5x + 3y =12 ] * 2 \[\rightarrow 10x +6y=24\] ........eq.(4)
[2x + 12y=81 ] *5 \[\rightarrow10x + 60y= 405\] ........eq.(5)

Answer 8

sorry there is 27 instead of 12 in equation (1)
u can do the corrections accordingly.................................................................................................................................................................................................................................................................................................................................................................................................................................**************************************************************************************************************************************////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////used for highlighting

Answer 9

subtract (4) from (5)
10x + 60 y = 405
10x + 6 y = 54
- - -
------------------
0 + 54y = 351
y = 6.5
put the value of y in eqn. (1)
you get
x = 1.5

Answer 10

hence rent of movie = $ 1.5
rent of video games = $ 6.5

Answer 11

hope you get the things....
if not understood, you can ask

Answer 12

thank you so much @lall