Solve {l}{7.4{(a+3)}=3.2a+43.2}{b=a}{c=b}{text{Solvefor}dtext{where}}{d=c}

$$\left. \begin{array} { l } { 7.4 {(a + 3)} = 3.2 a + 43.2 }\\ { b = a }\\ { c = b }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

Solve for a, b, c, d

$$d=5$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 7.4 by a+3.

$$7.4a+22.2=3.2a+43.2$$

Subtract 3.2a from both sides.

$$7.4a+22.2-3.2a=43.2$$

Combine 7.4a and -3.2a to get 4.2a.

$$4.2a+22.2=43.2$$

Subtract 22.2 from both sides.

$$4.2a=43.2-22.2$$

Subtract 22.2 from 43.2 to get 21.

$$4.2a=21$$

Divide both sides by 4.2.

$$a=\frac{21}{4.2}$$

Expand \frac{21}{4.2} by multiplying both numerator and the denominator by 10.

$$a=\frac{210}{42}$$

Divide 210 by 42 to get 5.

$$a=5$$

Consider the second equation. Insert the known values of variables into the equation.

$$b=5$$

Consider the third equation. Insert the known values of variables into the equation.

$$c=5$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$d=5$$

The system is now solved.

$$a=5 b=5 c=5 d=5$$