Solving Rational Equations

Let's analyze the given equation.

\frac{9 0}{1 0 0} = \frac{3 7 + x}{4 4 + x}

Here,

x

represents the number of consecutive successful satellite restarts the team at SRA needs to make to rise their success average to

90 % .

We are asked to find the value of

x .

\frac{9 0}{1 0 0} = \frac{3 7 + x}{4 4 + x}

Solve for

x

SimpQuotSimplify quotient

0.9 = \frac{3 7 + x}{4 4 + x}

LHS \cdot (44 + x) = RHS \cdot (44 + x)

0.9 (44 + x) = 37 + x

DistrDistribute

0.9

0.9 (44) + 0.9 (x) = 37 + x

39.6 + 0.9 x = 37 + x

LHS - 0.9 x = RHS - 0.9 x

39.6 = 37 + 0.1 x

LHS - 37 = RHS - 37

2.6 = 0.1 x

LHS / 0.1 = RHS / 0.1

26 = x

RearrangeEqnRearrange equation

x = 26

Therefore, the team at SRA needs to start

26

consecutive satellites to meet their goal.

Solving Rational Equations 1.10 - Solution