Solve 3/5*a+5/8*(a+1)=19

$$\frac { 3 } { 5 } \cdot a + \frac { 5 } { 8 } \cdot ( a + 1 ) = 19$$

Solve for a

$$a=15$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{8} by a+1.

$$\frac{3}{5}a+\frac{5}{8}a+\frac{5}{8}=19$$

Combine \frac{3}{5}a and \frac{5}{8}a to get \frac{49}{40}a.

$$\frac{49}{40}a+\frac{5}{8}=19$$

Subtract \frac{5}{8} from both sides.

$$\frac{49}{40}a=19-\frac{5}{8}$$

Convert 19 to fraction \frac{152}{8}.

$$\frac{49}{40}a=\frac{152}{8}-\frac{5}{8}$$

Since \frac{152}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49}{40}a=\frac{152-5}{8}$$

Subtract 5 from 152 to get 147.

$$\frac{49}{40}a=\frac{147}{8}$$

Multiply both sides by \frac{40}{49}, the reciprocal of \frac{49}{40}.

$$a=\frac{147}{8}\times \frac{40}{49}$$

Multiply \frac{147}{8} times \frac{40}{49} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{147\times 40}{8\times 49}$$

Do the multiplications in the fraction \frac{147\times 40}{8\times 49}.

$$a=\frac{5880}{392}$$

Divide 5880 by 392 to get 15.

$$a=15$$