Solve a/60+1/20left(20-aright)left(1+2.5right)leq64

$$\frac{ a }{ 60 } + \frac{ 1 }{ 20 } \left( 20-a \right) \left( 1+2.5 \right) \leq 64$$

Solve for a

$$a\geq -\frac{7260}{19}$$

Solution Steps

Multiply both sides of the equation by 60, the least common multiple of 60,20. Since 60 is positive, the inequality direction remains the same.

$$a+3\left(20-a\right)\left(1+2.5\right)\leq 3840$$

Add 1 and 2.5 to get 3.5.

$$a+3\left(20-a\right)\times 3.5\leq 3840$$

Multiply 3 and 3.5 to get 10.5.

$$a+10.5\left(20-a\right)\leq 3840$$

Use the distributive property to multiply 10.5 by 20-a.

$$a+210-10.5a\leq 3840$$

Combine a and -10.5a to get -9.5a.

$$-9.5a+210\leq 3840$$

Subtract 210 from both sides.

$$-9.5a\leq 3840-210$$

Subtract 210 from 3840 to get 3630.

$$-9.5a\leq 3630$$

Divide both sides by -9.5. Since -9.5 is negative, the inequality direction is changed.

$$a\geq \frac{3630}{-9.5}$$

Expand \frac{3630}{-9.5} by multiplying both numerator and the denominator by 10.

$$a\geq \frac{36300}{-95}$$

Reduce the fraction \frac{36300}{-95} to lowest terms by extracting and canceling out 5.

$$a\geq -\frac{7260}{19}$$