Solved on Sep 11, 2023

Find the mileage range where Company A's rental cost is no more than Company B's: $25 + 0.8m \leq 40 + 0.6m$

STEP 1

Assumptions1. Company A charges an initial fee of $25 and an additional80 cents for every mile driven. . Company B charges an initial fee of$ 40 and an additional60 cents for every mile driven.
3. We denote the number of miles driven by $m$ .
4. We are looking for the mileages for which Company A charges no more than Company B.

STEP 2

First, we need to write the cost function for each company. The cost function is the initial fee plus the cost per mile times the number of miles driven.
For Company A, the cost function is $Cost_A = \$25 +0.80m$ For Company B, the cost function is $Cost_B = \$40 +0.60m$

STEP 3

We are looking for the mileages for which Company A charges no more than Company B. This means that the cost function for Company A should be less than or equal to the cost function for Company B.
This gives us the inequality $Cost_A \leq Cost_B$

STEP 4

Substitute the cost functions of Company A and Company B into the inequality $\$25 +0.80m \leq \$40 +0.60m$

STEP 5

To simplify the inequality, we can subtract $0.60m$ from both sides $\$25 +0.20m \leq \$40$

STEP 6

Next, subtract $25 from both sides to isolate the term with$ m$0.20m \leq \$15

STEP 7

Finally, divide both sides by $0.20$ to solve for $m$ $m \leq \$15 /0.20$

STEP 8

Calculate the value of $m$ $m \leq75$ So, for mileages of75 miles or less, Company A will charge no more than Company B.

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Find the mileage range where Company A's rental cost is no more than Company B's: $25 + 0.8m \leq 40 + 0.6m$

STEP 1

STEP 2

First, we need to write the cost function for each company. The cost function is the initial fee plus the cost per mile times the number of miles driven.
For Company A, the cost function is $Cost_A = \$25 +0.80m$ For Company B, the cost function is $Cost_B = \$40 +0.60m$

STEP 3

We are looking for the mileages for which Company A charges no more than Company B. This means that the cost function for Company A should be less than or equal to the cost function for Company B.
This gives us the inequality $Cost_A \leq Cost_B$

STEP 4

Substitute the cost functions of Company A and Company B into the inequality $\$25 +0.80m \leq \$40 +0.60m$

STEP 5

To simplify the inequality, we can subtract $0.60m$ from both sides $\$25 +0.20m \leq \$40$

STEP 6

Next, subtract $25 from both sides to isolate the term with$ m$0.20m \leq \$15

STEP 7

Finally, divide both sides by $0.20$ to solve for $m$ $m \leq \$15 /0.20$

STEP 8

Calculate the value of $m$ $m \leq75$ So, for mileages of75 miles or less, Company A will charge no more than Company B.

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Find the mileage range where Company A's rental cost is no more than Company B's: 25+0.8m≤40+0.6m25 + 0.8m \leq 40 + 0.6m25+0.8m≤40+0.6m

STEP 1

STEP 2

STEP 3

We are looking for the mileages for which Company A charges no more than Company B. This means that the cost function for Company A should be less than or equal to the cost function for Company B.This gives us the inequalityCostA≤CostBCost_A \leq Cost_BCostA​≤CostB​

STEP 4

Substitute the cost functions of Company A and Company B into the inequality$25+0.80m≤$40+0.60m\$25 +0.80m \leq \$40 +0.60m$25+0.80m≤$40+0.60m

STEP 5

To simplify the inequality, we can subtract 0.60m0.60m0.60m from both sides$25+0.20m≤$40\$25 +0.20m \leq \$40$25+0.20m≤$40

STEP 6

Next, subtract 25frombothsidestoisolatethetermwith25 from both sides to isolate the term with 25frombothsidestoisolatethetermwithm$0.20m \leq \$15

STEP 7

Finally, divide both sides by 0.200.200.20 to solve for mmmm≤$15/0.20m \leq \$15 /0.20m≤$15/0.20

STEP 8

Calculate the value of mmmm≤75m \leq75m≤75So, for mileages of75 miles or less, Company A will charge no more than Company B.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the mileage range where Company A's rental cost is no more than Company B's: $25 + 0.8m \leq 40 + 0.6m$

We are looking for the mileages for which Company A charges no more than Company B. This means that the cost function for Company A should be less than or equal to the cost function for Company B.
This gives us the inequality $Cost_A \leq Cost_B$

Substitute the cost functions of Company A and Company B into the inequality $\$25 +0.80m \leq \$40 +0.60m$

To simplify the inequality, we can subtract $0.60m$ from both sides $\$25 +0.20m \leq \$40$

Next, subtract $25 from both sides to isolate the term with$ m$0.20m \leq \$15

Finally, divide both sides by $0.20$ to solve for $m$ $m \leq \$15 /0.20$

Calculate the value of $m$ $m \leq75$ So, for mileages of75 miles or less, Company A will charge no more than Company B.