One month Milan rented 2 movies and 6 video games for a total of $38 . The next month he rented 5 movies and 3 video games for a total of $32 . Find the rental cost for each movie and each video game.
One month Milan rented 2 movies and 6 video games for a total of $38 . The next month he rented 5 movies and 3 video games for a total of $32 . Find the rental cost for each movie and each video game
Let m=price per movie
Let v=price per video
2m + 6v=38, and
5m + 3v=32
Solve the following system:
{2 m+6 v = 38 | (equation 1)
5 m+3 v = 32 | (equation 2)
Swap equation 1 with equation 2:
{5 m+3 v = 32 | (equation 1)
2 m+6 v = 38 | (equation 2)
Subtract 2/5 × (equation 1) from equation 2:
{5 m+3 v = 32 | (equation 1)
0 m+(24 v)/5 = 126/5 | (equation 2)
Multiply equation 2 by 5/6:
{5 m+3 v = 32 | (equation 1)
0 m+4 v = 21 | (equation 2)
Divide equation 2 by 4:
{5 m+3 v = 32 | (equation 1)
0 m+v = 21/4 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{5 m+0 v = 65/4 | (equation 1)
0 m+v = 21/4 | (equation 2)
Divide equation 1 by 5:
{m+0 v = 13/4 | (equation 1)
0 m+v = 21/4 | (equation 2)
Collect results:
Answer: | m=13/4=$3.25 and v=21/4=$5.25
m=movie v=video
Then 2m + 6v = 38 and 5m + 3v = 32
Solve FIRST equation for v
6v=(38-2m)
v= (38-2m)/6 Substitue this into the SECOND equation and solve for 'm'
5m + 3 (38-2m)/6 =32
10m + 38 -2m = 64
8m= 26 or m= $ 3.25
Now sub into one of the two equations to find v
2(3.25) + 6v = 38
6v=31.5 or v = $ 5.25
