Solved on Mar 08, 2024

A phone company offers two plans: Plan A ( $25 +$ 0.07/min) and Plan B ( $16 +$ 0.11/min). Find the minutes and cost when the plans cost the same.
For what amount of calling do the two plans cost the same? $x$ minutes What is the cost when the two plans cost the same? $\$ \frac{25 - 16}{0.11 - 0.07}$

STEP 1

Assumptions
1. Plan A has a base cost of $25 and charges$ 0.07 per minute for calls.
2. Plan B has a base cost of $16 and charges$ 0.11 per minute for calls.
3. We are looking for the number of minutes where the cost of Plan A equals the cost of Plan B.

STEP 2

Let's denote the number of minutes of calls with the variable $m$ . We will set up an equation where the cost of Plan A equals the cost of Plan B.
$Cost\, of\, Plan\, A = Cost\, of\, Plan\, B$

STEP 3

Now, express the cost of Plan A as a function of $m$ .
$Cost\, of\, Plan\, A = 25 + 0.07m$

STEP 4

Express the cost of Plan B as a function of $m$ .
$Cost\, of\, Plan\, B = 16 + 0.11m$

STEP 5

Set the cost of Plan A equal to the cost of Plan B to find the value of $m$ where the costs are the same.
$25 + 0.07m = 16 + 0.11m$

STEP 6

Subtract $0.07m$ from both sides of the equation to get all the $m$ terms on one side.
$25 = 16 + 0.04m$

STEP 7

Subtract $16$ from both sides of the equation to isolate the term with $m$ .
$25 - 16 = 0.04m$

STEP 8

Calculate the left side of the equation.
$9 = 0.04m$

STEP 9

Divide both sides by $0.04$ to solve for $m$ .
$\frac{9}{0.04} = m$

STEP 10

Calculate the number of minutes $m$ .
$m = \frac{9}{0.04} = 225$
The two plans cost the same for 225 minutes of calls.

STEP 11

Now, we need to find the cost when the two plans cost the same. We can use either Plan A's or Plan B's cost formula and plug in $m = 225$ .
$Cost\, of\, Plan\, A = 25 + 0.07 \times 225$

STEP 12

Calculate the cost for Plan A when $m = 225$ .
$Cost\, of\, Plan\, A = 25 + 0.07 \times 225 = 25 + 15.75$

STEP 13

Calculate the total cost for Plan A.
$Cost\, of\, Plan\, A = 25 + 15.75 = \$40.75$
The cost when the two plans cost the same is $40.75.

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STEP 1

Assumptions
1. Plan A has a base cost of $25 and charges$ 0.07 per minute for calls.
2. Plan B has a base cost of $16 and charges$ 0.11 per minute for calls.
3. We are looking for the number of minutes where the cost of Plan A equals the cost of Plan B.

STEP 2

Let's denote the number of minutes of calls with the variable $m$ . We will set up an equation where the cost of Plan A equals the cost of Plan B.
$Cost\, of\, Plan\, A = Cost\, of\, Plan\, B$

STEP 3

Now, express the cost of Plan A as a function of $m$ .
$Cost\, of\, Plan\, A = 25 + 0.07m$

STEP 4

Express the cost of Plan B as a function of $m$ .
$Cost\, of\, Plan\, B = 16 + 0.11m$

STEP 5

Set the cost of Plan A equal to the cost of Plan B to find the value of $m$ where the costs are the same.
$25 + 0.07m = 16 + 0.11m$

STEP 6

Subtract $0.07m$ from both sides of the equation to get all the $m$ terms on one side.
$25 = 16 + 0.04m$

STEP 7

Subtract $16$ from both sides of the equation to isolate the term with $m$ .
$25 - 16 = 0.04m$

STEP 8

Calculate the left side of the equation.
$9 = 0.04m$

STEP 9

Divide both sides by $0.04$ to solve for $m$ .
$\frac{9}{0.04} = m$

STEP 10

Calculate the number of minutes $m$ .
$m = \frac{9}{0.04} = 225$
The two plans cost the same for 225 minutes of calls.

STEP 11

Now, we need to find the cost when the two plans cost the same. We can use either Plan A's or Plan B's cost formula and plug in $m = 225$ .
$Cost\, of\, Plan\, A = 25 + 0.07 \times 225$

STEP 12

Calculate the cost for Plan A when $m = 225$ .
$Cost\, of\, Plan\, A = 25 + 0.07 \times 225 = 25 + 15.75$

STEP 13

Calculate the total cost for Plan A.
$Cost\, of\, Plan\, A = 25 + 15.75 = \$40.75$
The cost when the two plans cost the same is $40.75.

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STEP 1

Assumptions1. Plan A has a base cost of 25andcharges25 and charges 25andcharges0.07 per minute for calls.2. Plan B has a base cost of 16andcharges16 and charges 16andcharges0.11 per minute for calls.3. We are looking for the number of minutes where the cost of Plan A equals the cost of Plan B.

STEP 2

Let's denote the number of minutes of calls with the variable mmm. We will set up an equation where the cost of Plan A equals the cost of Plan B.Cost of Plan A=Cost of Plan BCost\, of\, Plan\, A = Cost\, of\, Plan\, BCostofPlanA=CostofPlanB

STEP 3

Now, express the cost of Plan A as a function of mmm.Cost of Plan A=25+0.07mCost\, of\, Plan\, A = 25 + 0.07mCostofPlanA=25+0.07m

STEP 4

Express the cost of Plan B as a function of mmm.Cost of Plan B=16+0.11mCost\, of\, Plan\, B = 16 + 0.11mCostofPlanB=16+0.11m

STEP 5

Set the cost of Plan A equal to the cost of Plan B to find the value of mmm where the costs are the same.25+0.07m=16+0.11m25 + 0.07m = 16 + 0.11m25+0.07m=16+0.11m

STEP 6

Subtract 0.07m0.07m0.07m from both sides of the equation to get all the mmm terms on one side.25=16+0.04m25 = 16 + 0.04m25=16+0.04m

STEP 7

Subtract 161616 from both sides of the equation to isolate the term with mmm.25−16=0.04m25 - 16 = 0.04m25−16=0.04m

STEP 8

Calculate the left side of the equation.9=0.04m9 = 0.04m9=0.04m

STEP 9

Divide both sides by 0.040.040.04 to solve for mmm.90.04=m\frac{9}{0.04} = m0.049​=m

STEP 10

Calculate the number of minutes mmm.m=90.04=225m = \frac{9}{0.04} = 225m=0.049​=225The two plans cost the same for 225 minutes of calls.

STEP 11

Now, we need to find the cost when the two plans cost the same. We can use either Plan A's or Plan B's cost formula and plug in m=225m = 225m=225.Cost of Plan A=25+0.07×225Cost\, of\, Plan\, A = 25 + 0.07 \times 225CostofPlanA=25+0.07×225

STEP 12

Calculate the cost for Plan A when m=225m = 225m=225.Cost of Plan A=25+0.07×225=25+15.75Cost\, of\, Plan\, A = 25 + 0.07 \times 225 = 25 + 15.75CostofPlanA=25+0.07×225=25+15.75

STEP 13

Calculate the total cost for Plan A.Cost of Plan A=25+15.75=$40.75Cost\, of\, Plan\, A = 25 + 15.75 = \$40.75CostofPlanA=25+15.75=$40.75The cost when the two plans cost the same is $40.75.

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Assumptions
1. Plan A has a base cost of $25 and charges$ 0.07 per minute for calls.
2. Plan B has a base cost of $16 and charges$ 0.11 per minute for calls.
3. We are looking for the number of minutes where the cost of Plan A equals the cost of Plan B.

Let's denote the number of minutes of calls with the variable $m$ . We will set up an equation where the cost of Plan A equals the cost of Plan B.
$Cost\, of\, Plan\, A = Cost\, of\, Plan\, B$

Now, express the cost of Plan A as a function of $m$ .
$Cost\, of\, Plan\, A = 25 + 0.07m$

Express the cost of Plan B as a function of $m$ .
$Cost\, of\, Plan\, B = 16 + 0.11m$

Set the cost of Plan A equal to the cost of Plan B to find the value of $m$ where the costs are the same.
$25 + 0.07m = 16 + 0.11m$

Subtract $0.07m$ from both sides of the equation to get all the $m$ terms on one side.
$25 = 16 + 0.04m$

Subtract $16$ from both sides of the equation to isolate the term with $m$ .
$25 - 16 = 0.04m$

Calculate the left side of the equation.
$9 = 0.04m$

Divide both sides by $0.04$ to solve for $m$ .
$\frac{9}{0.04} = m$

Calculate the number of minutes $m$ .
$m = \frac{9}{0.04} = 225$
The two plans cost the same for 225 minutes of calls.

Now, we need to find the cost when the two plans cost the same. We can use either Plan A's or Plan B's cost formula and plug in $m = 225$ .
$Cost\, of\, Plan\, A = 25 + 0.07 \times 225$

Calculate the cost for Plan A when $m = 225$ .
$Cost\, of\, Plan\, A = 25 + 0.07 \times 225 = 25 + 15.75$

Calculate the total cost for Plan A.
$Cost\, of\, Plan\, A = 25 + 15.75 = \$40.75$
The cost when the two plans cost the same is $40.75.