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Anna007 [38]
3 years ago
14

Collin is building a deck on the back of his house. He has enough lumber for the deck to be 144 square feet. The length should b

e 10 feet more than its width.
What should the dimensions of the deck be?
Mathematics
1 answer:
joja [24]3 years ago
4 0
Width = x
length = x+10

Area of deck = 144 square feet

Area = length * width

144 = x(x+10)

Solving for x in a quadratic:

x²+10x = 144
x²+10x-144 = 0

Factor:
(x+18)(x-8) = 0

Solving for x:
x = 8, x = -18

Dimensions cannot be negative, therefore x = 8, only.

Length = x + 10
Length = 18

Width = 8
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Answer:

61.84%

Step-by-step explanation:

Let the cost of the box be x. Since the price of the box and the pen is Rs 80, the pen's price can be represented as 80 - x. The box is sold at a ten percent profit, and an added ten percent is equal to 1.1. Therefore, the price the box sells at is 1.1(x). A 20% loss is the same a keeping 80% or multiplying by 0.8. This means the pen sold at 0.8(80 - x). Now, we are given the box went for Rs 28 more than the pen, so we can create an equation:

1.1x = 0.8(80 - x) + 28

We can simplify and solve:

1.1x = 64 - 0.8x + 28

1.9x = 92

x = 92/1.9

x = 920/19

The cost of the box after the increase would be 1.1(920/19) and the pen would be 0.8(80 - 920/19).

The sum of these two can be written as a percent x of 80.

80x = 0.8(80 - 920/19) + 1.1(920/19)

80x = 64 - 0.8(920/19) + 1.1(920/9)

80x = 64 - 0.3(920/19)

80x = 64 - 276/19

80x = 940/19

x = 940/1520

x = 0.6184

This is 61.84%

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19. 

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This is the correct answer
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