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WARRIOR [948]
4 years ago
11

A party rental company has chairs and tables for rent.The total cost to rent 2 chairs and 5 tables is $35. The total cost to ren

t 8 chairs and 3 tables is $38.00. What is the cost to rent each chair and each table?
Mathematics
1 answer:
kvv77 [185]4 years ago
5 0

Answer: The cost of renting a chair is $2.5 while the cost of renting a table is $6

Step-by-step explanation: Let the cost chair rental be called h, while the cost of table rental shall be called t. To rent two chairs and five tables cost $35, so we can express this as

2h + 5t = 35

Also to rent eight chairs and three tables cost $38, and this too can be expressed as

8h + 3t = 38

We now have a pair of simultaneous equations as follows

2h + 5t = 35 ———(1)

8h + 3t = 38 ———(2)

We shall use the elimination method since all the unknown variables have coefficients greater than 1.

Multiply equation (1) by 8 and multiply equation (2) by 2. We now have

16h + 40t = 280 ———(3)

16h + 6t = 76 ———(4)

Subtract equation (4) from (3)

34t = 204

Divide both sides of the equation by 34

t = 6

Having calculated that, substitute for the value of t into equation (1)

2h + 5(6) = 35

2h + 30 = 35

Subtract 30 from both sides of the equation 2h = 5

Divide both sides of the equation by 2

h = 5/2 or (2.5)

Therefore the cost of rental for each chair (h) is $2.5 and the cost of rental for each table (t) is $6

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A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the poli
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Complete question:

A police car is located 50 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road.

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Step-by-step explanation:

Given

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Let x be how far the police is off the road.

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Let dx/dt be how fast the police is traveling toward the road.

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Recall that, h² = x² + y² (now differentiate with respect to time, t)

2h(dh/dt) = 2x(dx/dt) + 2y(dy/dt)

divide through by 2

h(dh/dt) = x(dx/dt) + y(dy/dt)

since the police car is not, dx/dt = 0

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139.284(75) = 50(0) + 130(dy/dt)

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dy/dt = 10446.3 / 130

dy/dt = 80.356 ft/s

Therefore, the red car is traveling along the road at 80.356 ft/s

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