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Noelle and Micah went to the bank to open new checking accounts. The equation C=0.2n+1.20 represents the monthly cost, C, in dollars, where n is the number of checks written by Noelle. In Micah's account, the monthly cost is proportional to the number of checks written. The monthly cost for Micah's account is $1.20 for writing 3 checks. How many checks must Noelle and Micah write, if any, so that the cost of the accounts is the same for one month? What is the cost, if any?

User Chardy
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1 Answer

5 votes
5 votes

Answer:

C = $2.40

n = 6

Explanation:

For Noelle,

Equation that represents the monthly cost 'C',

C = 0.2n + 1.20

Here, n = number of checks written in a month

For Micah,

Monthly cost for writing checks 'C' = $1.20

Number of checks 'n' = 3

Since, Cost of writing checks ∝ Number of checks written

C' ∝ n

C' = kn

k =
(C')/(n)

Here, k = proportionality constant

For C' = 1.2 and n = 3

k =
(1.2)/(3)

k = 0.4

Equation will be,

C' = 0.4n

For any month C = C'

Therefore, 0.2n + 1.20 = 0.4n

0.4n - 0.2n = 1.20

0.2n = 1.20

n = 6

Number of checks written by Noelle and Micah = 6

For n = 6,

C = 0.2(6) + 1.20

C = $2.40

Cost of writing checks = $2.40

User TheKidsWantDjent
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