Question

the answer and the work

Answer 1

Step-by-step explanation:

Let's let $T$ represent the cost of tapes, and $C$ be the cost of CDs.

From the problem statement, we can create the following two equations:

$4T + 2C = 46$

$3T + C = 28$

To solve this system of equations, we can solve for $C$ in the second equation and substitute into the first equation to get the value of $T$:

$3T + C = 28$

$C = 28 - 3T$

Substitution:

$4T + 2(28 - 3T) = 46$

$4T + 56 - 6T = 46$

$-2T = -10$

$T = 5$

Now that we know the cost of the tapes, we can plug this value into either equation to get the cost of CDs:

$4T + 2C = 46$

$4(5) + 2C = 46$

$20 + 2C = 46$

$2C = 26$

$C = 13$

or

$3T + C = 28$

$3(5) + C = 28$

$15 + C = 28$

$C = 13$

Therefore, the cost of a tape is $5$ and the cost of a CD is $13$.