Solve 16/5a+37/10(25-a)leq50

$$\frac { 16 } { 5 } a + \frac { 37 } { 10 } ( 25 - a ) \leq 50$$

Solve for a

$$a\geq 85$$

Solution Steps

Use the distributive property to multiply \frac{37}{10} by 25-a.

$$\frac{16}{5}a+\frac{37}{10}\times 25+\frac{37}{10}\left(-1\right)a\leq 50$$

Express \frac{37}{10}\times 25 as a single fraction.

$$\frac{16}{5}a+\frac{37\times 25}{10}+\frac{37}{10}\left(-1\right)a\leq 50$$

Multiply 37 and 25 to get 925.

$$\frac{16}{5}a+\frac{925}{10}+\frac{37}{10}\left(-1\right)a\leq 50$$

Reduce the fraction \frac{925}{10} to lowest terms by extracting and canceling out 5.

$$\frac{16}{5}a+\frac{185}{2}+\frac{37}{10}\left(-1\right)a\leq 50$$

Multiply \frac{37}{10} and -1 to get -\frac{37}{10}.

$$\frac{16}{5}a+\frac{185}{2}-\frac{37}{10}a\leq 50$$

Combine \frac{16}{5}a and -\frac{37}{10}a to get -\frac{1}{2}a.

$$-\frac{1}{2}a+\frac{185}{2}\leq 50$$

Subtract \frac{185}{2} from both sides.

$$-\frac{1}{2}a\leq 50-\frac{185}{2}$$

Convert 50 to fraction \frac{100}{2}.

$$-\frac{1}{2}a\leq \frac{100}{2}-\frac{185}{2}$$

Since \frac{100}{2} and \frac{185}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}a\leq \frac{100-185}{2}$$

Subtract 185 from 100 to get -85.

$$-\frac{1}{2}a\leq -\frac{85}{2}$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}. Since -\frac{1}{2} is negative, the inequality direction is changed.

$$a\geq -\frac{85}{2}\left(-2\right)$$

Express -\frac{85}{2}\left(-2\right) as a single fraction.

$$a\geq \frac{-85\left(-2\right)}{2}$$

Multiply -85 and -2 to get 170.

$$a\geq \frac{170}{2}$$

Divide 170 by 2 to get 85.

$$a\geq 85$$