Answer:
The cost of 1 videotape = $ 3.4
Step-by-step explanation:
Let us assume the cost of each cassette tap = $ m
So, the cost of each videotape = 2 x ( Cost of 1 cassette) = 2 x m = 2 m
Now, the cost of 3 cassette tap = 3 x ( Cost of 1 cassette) = 3 x m = 3 m
Also, the cost of 5 videotape = 5 x ( Cost of 5 videotape) = 5 x (2m) = 10 m
So, the cost of 3 cassette tap + 5 videotape = 3 m + 10 m
Also, given 3 blank cassette tapes and 5 blank videotapes costs $22.10 .
⇒ 3 m + 10 m = $22.10
or, 13 m = 22.10
⇒ m = 22.10/13 =1.7
or, m = $1.7
Hence, the cost of 1 cassette = m = $1.7
And, the cost of 1 videotape = 2 m = 2x ($1.7) = $ 3.4
Answer:
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
Step-by-step explanation:
