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As a part of a social studies class project on economics, anette and Jeff are researching the benifits of membership in an online music club. yearly membership with the online music. lub costs $48. Members pay $0.99 per song to download music. Nonmembers may download songs for $1.29 each. Write an equation to represent the point at which the total cost of downloading songs as a club member is equal to the total cost of downloading songs as a nonmember.

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merlynthewhizz
Let the number of music downloaded by the member be 'x'

Downloading one music for member = $0.99
Downloading two pieces of music for member = 2 × 0.99
Downloading three pieces of music for member = 3 × 0.99
Downloading 'x' pieces of music for member = x × 0.99 = 0.99x

Plus the membership club fee of $48

The expression of the total amount of fee charged to a member for 'x' pieces of music downloaded = $48 + 0.99x

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Let 'x' be the number of pieces of music downloaded by a non-member.
The total cost of downloading 'x' pieces of music is 1.29x

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Cost downloading as member = Cost downloading as non-member
48 + 0.99x = 1.29x
48 = 1.29x - 0.99x 
48 = 0.3x


fichoh

The equation which relates the point at which the cost as member and non-member equals is 48 + 0.99n = 1.29n

Let :

  • number of songs downloaded = n

Cost as a Member :

  • Membership fee = $48
  • Cost per download = $0.99
  • Total cost = 48 + 0.99n

Cost as a non-member :

  • Cost per download = $1.29
  • Total cost = 1.29n

The point at which total cost expended as a member equals that of a non-member can be expressed thus :

  • Total cost as member = Total cost as non-member
  • 48 + 0.99n = 1.29n

Therefore, the required expression is 48 + 0.99n = 1.29n

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