Question

The running time for movie A is 33 mins more than twice the running time for movie B. If the running time for movie A is subtracted from triple the running time for movie B, the result is 57 mins. find the running time for each movie..

Movie A-
Movie B-

Answer 1

use what they tell you to create the equations

a=33+2b & 57=3b-a

for this to work we need to substitute a variable to get rid of it.
look at
57=3b-a (lets switch it around s that the equation reads "a=")
57+a=3b
a=3b-57 (this is our new equations)

so now we know that
a=33+2b & a=3b-57
so we can write 33+2b=3b-57. we have now "gotten rid" of "a"

SOLVE FOR B

33+2b=3b-57 (get variable alone)
33= 3b-2b-57 (subtract and add accordingly)
33= b-57
33+57=b
90=b (this means that movie b is 90 long)

SOLVE FOR A

you can plug "b" into any of the original equations.

a=33+2b
a=33+2(90)
a=33+180
a=213

CHECK

plug "a" into any of the original equations to find "b" if b=90 then you know you've done it right

213=33+2b
213-33=2b
180=2b
180/2=b
90=b

hope this helps :)

Answer 2

X is the running time for movie A and y the running time for movie B
X = 2y + 33
3y - × = 57
x- 2y = 33
-× + 3y = 57 => y = 90
=> x 33 + 180 = 213