Solve 35+4*25(60-m)+m(3*25+3*35)leq9900

$$35 + 4 \times 25 ( 60 - m ) + m ( 3 \times 25 + 3 \times 35 ) \leq 9900$$

Solve for m

$$m\leq \frac{773}{16}$$

Solution Steps

Multiply 4 and 25 to get 100.

$$35+100\left(60-m\right)+m\left(3\times 25+3\times 35\right)\leq 9900$$

Use the distributive property to multiply 100 by 60-m.

$$35+6000-100m+m\left(3\times 25+3\times 35\right)\leq 9900$$

Add 35 and 6000 to get 6035.

$$6035-100m+m\left(3\times 25+3\times 35\right)\leq 9900$$

Multiply 3 and 25 to get 75. Multiply 3 and 35 to get 105.

$$6035-100m+m\left(75+105\right)\leq 9900$$

Add 75 and 105 to get 180.

$$6035-100m+m\times 180\leq 9900$$

Combine -100m and m\times 180 to get 80m.

$$6035+80m\leq 9900$$

Subtract 6035 from both sides.

$$80m\leq 9900-6035$$

Subtract 6035 from 9900 to get 3865.

$$80m\leq 3865$$

Divide both sides by 80. Since 80 is positive, the inequality direction remains the same.

$$m\leq \frac{3865}{80}$$

Reduce the fraction \frac{3865}{80} to lowest terms by extracting and canceling out 5.

$$m\leq \frac{773}{16}$$