One month Dan rented 2 movies and 5 video games for a total of $35. The next month he rented 8 movies and 3 video games for a total of $38. Find the rental cost for each movie and each video game.

Answer 1

2M + 5V = 35

8M + 3V = 38

Multiply 1st equation by 4, then subtract the 2nd equation from it to eliminate one variable

8M + 20V = 140

8M + 3V = 38

17V = 102

V = 102/17 = $6 per video

2M = 35-5(6) = 5

M= 5/2 = $2.50 per movie

Answer 2

If m represents the cost of a movie rental and g represents the cost of a video game rental, then we can write two equations:

2m+5g=$35

8m+3g=$38

Now if we subtract 5g from both sides of the first equation, we get

2m=$35-5g

Then, dividing by 2, we get

m=$17.50-2.5g.

Now substitute into the second equation to get

8($17.50-2.5g)+3g=$38

Distribute to get

$140-20g+3g=$38

$140-17g=$38

Add 17g-$38 to each side to get

$140-$38=17g

17g=$102

g=$6

Substitute back into the first equation to get

2m+5($6)=$35

2m+$30=$35

Subtract $30 from both sides to get

2m=$5

Divide by 2 to get

m=$2.50

So we have that a movie rental costs $4.75, and a video game rental costs $5.10. We check our work by substituting into both equations.

2($2.50)+5($6)=$35

$5+$30=$35

This is correct, and

8($2.50)+3($6)=$38

$20+$18=$38.

This is also correct, so we have the correct values.

Answer 3

Answer 4

See the previous.