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Math

QuestionAfter how many months will Bob's old internet (65−5065 - 50) equal the new provider's (150+40×150 + 40 \times months)?

Studdy Solution

STEP 1

Assumptions1. The old internet provider charges 65permonthandoffersa65 per month and offers a 50 customer loyalty credit. . The new internet provider charges a one-time installation fee of 150and150 and 40 per month.
3. We need to find the number of months after which the cost of both options will be equal.

STEP 2

First, we need to calculate the monthly cost for the old internet provider. This can be done by subtracting the customer loyalty credit from the monthly fee.
Old provider cost=Monthly fee−Customer loyalty creditOld\, provider\, cost = Monthly\, fee - Customer\, loyalty\, credit

STEP 3

Now, plug in the given values for the monthly fee and customer loyalty credit to calculate the cost for the old provider.
Old provider cost=$65−$50Old\, provider\, cost = \$65 - \$50

STEP 4

Calculate the monthly cost for the old internet provider.
Old provider cost=$65−$50=$15Old\, provider\, cost = \$65 - \$50 = \$15

STEP 5

Now, we need to calculate the total cost for each provider after 'n' months. For the old provider, this is simply the monthly cost times the number of months.
Old provider total cost=Old provider costtimesnOld\, provider\, total\, cost = Old\, provider\, cost \\times n

STEP 6

For the new provider, the total cost includes the one-time installation fee plus the monthly fee times the number of months.
New provider total cost=Installation fee+(Monthly feetimesn)New\, provider\, total\, cost = Installation\, fee + (Monthly\, fee \\times n)

STEP 7

We need to find the number of months 'n' after which the total cost for both providers will be the same. This gives us the equationOld provider total cost=New provider total costOld\, provider\, total\, cost = New\, provider\, total\, cost

STEP 8

Substitute the expressions for the total cost of both providers into the equation.
Old provider costtimesn=Installation fee+(Monthly feetimesn)Old\, provider\, cost \\times n = Installation\, fee + (Monthly\, fee \\times n)

STEP 9

Substitute the known values into the equation.
$15timesn=$150+($40timesn)\$15 \\times n = \$150 + (\$40 \\times n)

STEP 10

Rearrange the equation to isolate 'n' on one side.
$15n−$40n=$150\$15n - \$40n = \$150

STEP 11

implify the equation.
−$25n=$150-\$25n = \$150

STEP 12

olve for 'n'.
n=$150/−$25n = \$150 / -\$25

STEP 13

Calculate the number of months.
n=$150/−$25=−6n = \$150 / -\$25 = -6Since the number of months cannot be negative, we take the absolute value of 'n'.
n=∣−6∣=6n = | -6 | =6So, the two options would cost the same after6 months.

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