Solve a b c=180;c=10a;a= 1/4 b - ScanMath

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Type your math problem... a b c=180;c=10a;a= 1/4 b

Question

Solve the system of equations

(a, b, c) = (\frac{3 36}{2}, 2336, 5336)

Alternative Form

(a, b, c) \approx (1.650964, 6.603854, 16.509636)

Evaluate

⎩ ⎨ ⎧ ab c = 180 c = 10 a a = \frac{1}{4} b

Substitute the given value of c into the equation {ab c = 180 a = \frac{1}{4} b

{ab \times 10 a = 180 a = \frac{1}{4} b

Simplify

More Steps

{10 a^{2} b = 180 a = \frac{1}{4} b

Substitute the given value of a into the equation 10 a^{2} b = 180

10 (\frac{1}{4} b)^{2} b = 180

Simplify

More Steps

\frac{5 b ^{3}}{8} = 180

Cross multiply

5 b^{3} = 8 \times 180

Simplify the equation

5 b^{3} = 1440

Divide both sides

\frac{5 b ^{3}}{5} = \frac{1440}{5}

Divide the numbers

b^{3} = \frac{1440}{5}

Divide the numbers

More Steps

b^{3} = 288

Take the 3 -th root on both sides of the equation

3 b^{3} = 3288

Calculate

b = 3288

Simplify the root

More Steps

b = 2336

Substitute the given value of b into the equation a = \frac{1}{4} b

a = \frac{1}{4} \times 2336

Calculate

a = \frac{3 36}{2}

Substitute the given value of a into the equation c = 10 a

c = 10 \times \frac{3 36}{2}

Calculate

c = 5336

Calculate

⎩ ⎨ ⎧ a = \frac{3 36}{2} b = 2336 c = 5336

Check the solution

More Steps

⎩ ⎨ ⎧ a = \frac{3 36}{2} b = 2336 c = 5336

Solution

(a, b, c) = (\frac{3 36}{2}, 2336, 5336)

Alternative Form

(a, b, c) \approx (1.650964, 6.603854, 16.509636)

Show Solution