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2 years ago

A washer and a dryer cost $911 combined. The washer costs $39 less than the dryer. What is the cost of the dryer?

Mathematics

2 answers:

Gemiola [76]2 years ago

3 0

$475 is the dryer, and the washer is $436

Vikki [24]2 years ago

3 0

Sum and difference problem, where difference = larger number - smaller number.

The larger number is (sum+difference)/2.
The smaller number is (sum - difference)/2

Therefore the dryer costs (911+39)/2=475
The washer costs (911-39)/2=436

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Step-by-step explanation:

Refer to the attached diagram:

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$Width = 3 - 2x \\\\$

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$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

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$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

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$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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$V = \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

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The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

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