Solve y/60*0.5+3600-y/50*1.2leq40

$$\frac { y } { 60 } \times 0.5 + \frac { 3600 - y } { 50 } \times 1.2 \leq 40$$

Solve for y

$$y\geq \frac{139200}{47}$$

Solution Steps

Multiply both sides of the equation by 300, the least common multiple of 60,50. Since 300 is positive, the inequality direction remains the same.

$$5y\times 0.5+6\left(3600-y\right)\times 1.2\leq 12000$$

Multiply 5 and 0.5 to get 2.5.

$$2.5y+6\left(3600-y\right)\times 1.2\leq 12000$$

Multiply 6 and 1.2 to get 7.2.

$$2.5y+7.2\left(3600-y\right)\leq 12000$$

Use the distributive property to multiply 7.2 by 3600-y.

$$2.5y+25920-7.2y\leq 12000$$

Combine 2.5y and -7.2y to get -4.7y.

$$-4.7y+25920\leq 12000$$

Subtract 25920 from both sides.

$$-4.7y\leq 12000-25920$$

Subtract 25920 from 12000 to get -13920.

$$-4.7y\leq -13920$$

Divide both sides by -4.7. Since -4.7 is negative, the inequality direction is changed.

$$y\geq \frac{-13920}{-4.7}$$

Expand \frac{-13920}{-4.7} by multiplying both numerator and the denominator by 10.

$$y\geq \frac{-139200}{-47}$$

Fraction \frac{-139200}{-47} can be simplified to \frac{139200}{47} by removing the negative sign from both the numerator and the denominator.

$$y\geq \frac{139200}{47}$$