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QuestionFind the minutes where Plan A (29+0.09m29 + 0.09m) equals Plan B (0.14m0.14m) and the cost at that point.

Studdy Solution

STEP 1

Assumptions1. Plan A costs 29initiallyandanadditional29 initially and an additional 0.09 for each minute of calls. . Plan B has no initial fee but costs $0.14 for each minute of calls.
3. We want to find the amount of calling (in minutes) where the two plans cost the same.

STEP 2

We can set up an equation where the cost of Plan A equals the cost of Plan B.PlanA=PlanBPlan A = Plan B

STEP 3

Substitute the given costs into the equation.$29+$0.09×minutes=$0.14×minutes\$29 + \$0.09 \times minutes = \$0.14 \times minutes

STEP 4

Rearrange the equation to isolate the variable 'minutes' on one side.$0.14×minutes−$0.09×minutes=$29\$0.14 \times minutes - \$0.09 \times minutes = \$29

STEP 5

Combine like terms on the left side of the equation.
$0.05×minutes=$29\$0.05 \times minutes = \$29

STEP 6

To solve for 'minutes', divide both sides of the equation by $0.05.
minutes=$29$0.05minutes = \frac{\$29}{\$0.05}

STEP 7

Calculate the value for 'minutes'.
minutes=$29$0.05=580minutes = \frac{\$29}{\$0.05} =580So, the two plans cost the same for580 minutes of calling.

STEP 8

We also want to find the cost when the two plans cost the same. We can substitute the value of 'minutes' into either of the original cost equations. Let's use Plan A.
Cost=$29+$0.09×minutesCost = \$29 + \$0.09 \times minutes

STEP 9

Substitute the value for 'minutes' into the equation.
Cost=$29+$.09×580Cost = \$29 + \$.09 \times580

STEP 10

Calculate the cost.
Cost=$29+$0.09×580=$81.20Cost = \$29 + \$0.09 \times580 = \$81.20So, the cost when the two plans cost the same is $81.20.

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