QuestionFind when the costs of renting a rug cleaner from Company A: \$22 + \$6h and Company B: \$28 + \$4h are equal.

Studdy Solution

STEP 1

Assumptions1. Company A charges a fixed fee of $22 and an hourly fee of$ 6. Company B charges a fixed fee of $28 and an hourly fee of$ 43. We need to find the number of hours (h) for which the total cost of renting the machine from both companies will be the same

STEP 2

First, let's set up an equation for the total cost of renting the machine from Company A.
$Cost_{A} = Fixed\, fee_{A} + Hourly\, fee_{A} \\times Hours$

STEP 3

Now, plug in the given values for the fixed fee and hourly fee of Company A into the equation.
$Cost_{A} = \$22 + \$6 \\times h$

STEP 4

Next, let's set up an equation for the total cost of renting the machine from Company B.
$Cost_{B} = Fixed\, fee_{B} + Hourly\, fee_{B} \\times Hours$

STEP 5

Now, plug in the given values for the fixed fee and hourly fee of Company B into the equation.
$Cost_{B} = \$28 + \$4 \\times h$

STEP 6

To find the number of hours for which the total cost of renting the machine from both companies will be the same, we set the two cost equations equal to each other.
$Cost_{A} = Cost_{B}$

STEP 7

Substitute the cost equations for Company A and Company B into the equation.
$\$22 + \$6 \\times h = \$28 + \$4 \\times h$

STEP 8

To solve for h, we first subtract $4h$ from both sides of the equation.
$\$22 + \$6 \\times h - \$4 \\times h = \$28 + \$4 \\times h - \$4 \\times h$

STEP 9

implify the equation.
$\$22 + \$2 \\times h = \$28$

STEP 10

Next, subtract $22 from both sides of the equation.
$\$22 + \$2 \\times h - \$22 = \$28 - \$22$

STEP 11

implify the equation.
$\$ \\times h = \$6$

STEP 12

Finally, divide both sides of the equation by2 to solve for h.
$h = \$6 / \$2$

STEP 13

Calculate the number of hours.
$h = \$6 / \$2 =3\, hours$

STEP 14

Now that we have the number of hours, we can calculate the total amount spent at each company by substituting h =3 into the cost equations for Company A and Company B.
$Cost_{A} = \$22 + \$6 \\times3$ $Cost_{B} = \$28 + \$4 \\times3$

STEP 15

Calculate the total amount spent at each company.
$Cost_{A} = \$22 + \$ \\times3 = \$40$ $Cost_{B} = \$28 + \$4 \\times3 = \$40$ After3 hours of use, the total amount spent at each company will be the same, which is $40.

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