Amusic store is offering a frequent buyers club membership. the membership costs $22 per year, and then a member can buy cds at a reduced price. if a member buys 17 cds in one year, the cost is $111.25. determine the cost of each cd for a member.

the cost of each CD for a member is $5.25

Step-by-step explanation:

The membership costs $22 per year, and then a member can buy CDs at a reduced price.

Let x represent the cost of each CD for a member.

Let n represent the number of CDs that each member buys. This means that the total cost of buying n CDs for a member for a year would be

22 + nx

If a member buys 17 CDs in one year, the cost is $111.25. This means that

17x + 22 = 111.25

17x = 111.25 - 22 = 89.25

x = 89.25/175 = 5.25

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .