Solve 4000(20-a)+2500(30+2a)leq1600

$$4000 ( 20 - a ) + 2500 ( 30 + 2 a ) \leq 1600$$

Solve for a

$$a\leq -\frac{767}{5}$$

Solution Steps

Use the distributive property to multiply 4000 by 20-a.

$$80000-4000a+2500\left(30+2a\right)\leq 1600$$

Use the distributive property to multiply 2500 by 30+2a.

$$80000-4000a+75000+5000a\leq 1600$$

Add 80000 and 75000 to get 155000.

$$155000-4000a+5000a\leq 1600$$

Combine -4000a and 5000a to get 1000a.

$$155000+1000a\leq 1600$$

Subtract 155000 from both sides.

$$1000a\leq 1600-155000$$

Subtract 155000 from 1600 to get -153400.

$$1000a\leq -153400$$

Divide both sides by 1000. Since 1000 is positive, the inequality direction remains the same.

$$a\leq \frac{-153400}{1000}$$

Reduce the fraction \frac{-153400}{1000} to lowest terms by extracting and canceling out 200.

$$a\leq -\frac{767}{5}$$