Solve 500x+400(-5/3x+18)+250(2/3x+2)

$$500x+400(- \frac{ 5 }{ 3 } x+18)+250( \frac{ 2 }{ 3 } x+2)$$

Evaluate

$$7700$$

Solution Steps

Use the distributive property to multiply 400 by -\frac{5}{3}x+18.

$$500x+400\left(-\frac{5}{3}\right)x+7200+250\left(\frac{2}{3}x+2\right)$$

Express 400\left(-\frac{5}{3}\right) as a single fraction.

$$500x+\frac{400\left(-5\right)}{3}x+7200+250\left(\frac{2}{3}x+2\right)$$

Multiply 400 and -5 to get -2000.

$$500x+\frac{-2000}{3}x+7200+250\left(\frac{2}{3}x+2\right)$$

Fraction \frac{-2000}{3} can be rewritten as -\frac{2000}{3} by extracting the negative sign.

$$500x-\frac{2000}{3}x+7200+250\left(\frac{2}{3}x+2\right)$$

Combine 500x and -\frac{2000}{3}x to get -\frac{500}{3}x.

$$-\frac{500}{3}x+7200+250\left(\frac{2}{3}x+2\right)$$

Use the distributive property to multiply 250 by \frac{2}{3}x+2.

$$-\frac{500}{3}x+7200+250\times \frac{2}{3}x+500$$

Express 250\times \frac{2}{3} as a single fraction.

$$-\frac{500}{3}x+7200+\frac{250\times 2}{3}x+500$$

Multiply 250 and 2 to get 500.

$$-\frac{500}{3}x+7200+\frac{500}{3}x+500$$

Combine -\frac{500}{3}x and \frac{500}{3}x to get 0.

$$7200+500$$

Add 7200 and 500 to get 7700.

$$7700$$

Factor

$$2^{2}\times 5^{2}\times 7\times 11$$

Solution Steps

Factor out \frac{100}{3}.

$$\frac{100\left(15x+4\left(-5x+54\right)+5\left(x+3\right)\right)}{3}$$

Simplify.

$$7700$$