math question system of equations

Question

Melinda purchased 3 blank cassette tapes and 5 blank videotapes for a total of $22.10 not including tax. if each videotape cost twice the price of cassette tape, what did Melinda pay for 1 videotape?

Answer 1

Let's let c represent the cost of one cassette tape and v represent the cost of one videotape. Then since each videotape cost twice that of the cassette tape, we can write the following equation:

v = 2c

Then since the total spent on both was $22.10 and 3 cassette tapes and 5 videotapes were purchased, we can also write:

3c + 5v = $22.10

If we substitute 2c for v in our second equation, we can find the value of c (or the cost of one cassette tape):

3c + 5(2c) = 22.10

Combine like terms and use inverse operations to solve for c:

3c + 10c = 22.10

13c = 22.10

13c/13 = 22.10/13

c = $1.70

So the cost of 1 cassette tape is $1.70

A videotape cost twice that (v = 2c) :

v = 2 * $1.70

v = $3.40

So the cost of one videotape is $3.40

To check, the cost of 3 cassette tapes and 5 videotapes would be:

3 * $1.70 + 5 * $3.40 =

$5.10 + $17.00 =

$22.10