Question

It costs Trevor $50 to have a security system installed in his house. He pays a monthly service fee plus tax of 6% of his monthly bill. After 6 months, Trevor had paid a total of $361.64 for his service fee, taxes, and his initial installation. Trevor’s monthly service fee, not including taxes, is ___.

Answer 1

$49

Explanation:

Cost of security system installation = $50

Let the monthly service cost be $x

• In 6 month monthly service cost = 6*$x= $6x

tax percentage = 6% of monthly service cost

hence if monthly service cost is $x

Then Tax value in terms of x is = 6% of $x = 6/100 * $x =$ 0.06x

• In 6 month, Tax value in terms of x = 6 * $0.06x = $.36x

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Therefore total cost incurred by Trevor in 6 month including installation charges =

6 month monthly service cost + Tax value in 6 month + installation cost

Substituting value of 6 month monthly service cost , Tax value in 6 month , installation cost in above expression we have

Therefore total cost incurred by Trevor in 6 month including installation charges = $6x+ $0.36x+ $50 = $6.36x + $50

But it is given that After 6 months, Trevor had paid a total of $361.64 for his service fee, taxes, and his initial installation

Therefore total cost incurred by Trevor in 6 month including installation charges is also equal to $361.64

Hence,

$6.36x + $50 = $361.64

=> $6.36x = $361.64 - $50

=>$6.36x = $311.64

=> x = $311.64/6.36

=> x = 49.

Therefore , Trevor’s monthly service fee, not including taxes is $X which is equal to $49.