Question

Ok i understood it finally in regular problems but they had to go and give me a word problem and im confused now i thought i started it right but when i keep working through it i get no answers that match the possible ones

Answer 1

Gina, Sam and Robby all rented movies from the same video store. They each rented some dramas, comedies and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?

3 dramas, 5 comedies and 3 documentaries

2 dramas, 6 comedies and 3 documentaries

1 dramas, 4 comedies and 6 documentaries

4 dramas, 3 comedies and 4 documentaries

Answer 2

I have to use substitution or elimnation

Answer 3

i started out with these equations from it :
a+b+c=11
2a+3b+2c=27
a+2b+2c=19
but, im not sure if these are right or not

Answer 4

Or at least tell me if i started it off right with those equations ^^^^

Answer 5

Let x represent the number of dramas
Let y represent the number of comedies
Let z represent the number of documentaries

Gina: x + y + z = 11
Sam: 2x + 3y + 2z = 27
Robby: x + 2y +2z = 19

Answer 6

a basically used a b and c but ok

Answer 7

Rearrange the first equation for x:

x = 11 - y - z

Answer 8

ok

Answer 9

After rearranging you can put this equation in (2) or (3) and eliminate for y or z.

Substitute x = 11 - y - z into (2)
2(11 - y - z) + 3y + 2z = 27
22 - 2y - 2z + 3y + 2z = 27
y = 27 - 22
y = 5

YAY that's the value of y :P

Substitute y = 5 into (1)
x + y + z = 11
x + 5 + z = 11
x + z = 6
x = 6 - z

Substitute x = 6 - z and y = 5 into (3)
x + 2y + 2z = 19
6 - z + 2y + 2z = 19
2y + z = 13
z = 13 - 2y
z = 13 - 2(5)
z = 3

There's your "z" value

Substitute y = 5 and z = 3 into (1) to solve for x
x + y + z = 11
x + 5 + 3 = 11
x = 11 - 8
x = 3

Check if your values satisfy the equation:

LS = 2x + 3y + 2z
= 2(3) + 3(5) + 2(3)
= 6 + 15 + 6
= 27

RS = 27

Since LS = RS, the values of x, y and z satisfy the equation. Therefore, x = 3, y = 5 and z = 3.

WELL?

Answer 10

wow thank you so much

Answer 11

ahah no problem. my back hurts now

Answer 12

awe im sorry :(

Answer 13

aha no worries.

Answer 14

ok and that is what some good ole ibuprofen is for

Answer 15

huh, yeah sure. :P