Solve 15a+5(100-a)leq0.3[45+25(100-a))

$$15 a + 5 ( 100 - a ) \leq 0.3 [ 45 + 25 ( 100 - a ) )$$

Solve for a

$$a\leq \frac{527}{35}$$

Solution Steps

Use the distributive property to multiply 5 by 100-a.

$$15a+500-5a\leq 0.3\left(45+25\left(100-a\right)\right)$$

Combine 15a and -5a to get 10a.

$$10a+500\leq 0.3\left(45+25\left(100-a\right)\right)$$

Use the distributive property to multiply 25 by 100-a.

$$10a+500\leq 0.3\left(45+2500-25a\right)$$

Add 45 and 2500 to get 2545.

$$10a+500\leq 0.3\left(2545-25a\right)$$

Use the distributive property to multiply 0.3 by 2545-25a.

$$10a+500\leq 763.5-7.5a$$

Add 7.5a to both sides.

$$10a+500+7.5a\leq 763.5$$

Combine 10a and 7.5a to get 17.5a.

$$17.5a+500\leq 763.5$$

Subtract 500 from both sides.

$$17.5a\leq 763.5-500$$

Subtract 500 from 763.5 to get 263.5.

$$17.5a\leq 263.5$$

Divide both sides by 17.5. Since 17.5 is positive, the inequality direction remains the same.

$$a\leq \frac{263.5}{17.5}$$

Expand \frac{263.5}{17.5} by multiplying both numerator and the denominator by 10.

$$a\leq \frac{2635}{175}$$

Reduce the fraction \frac{2635}{175} to lowest terms by extracting and canceling out 5.

$$a\leq \frac{527}{35}$$