Exercise 28 Page p22

We can use the percent proportion to find the number of questions Kara need to answer correctly. The percent proportion is a proportion that equates a part of a whole to a percent out of

100 .

\frac{part}{whole} = \frac{percent}{1 0 0} \Leftrightarrow \frac{a}{b} = \frac{p}{1 0 0}

The total number of questions is the whole and the number of correctly answered questions is the part. Since we know that she need to get a

75 %

of

35

questions, we can substitute

b = 35

and

p = 75

into the formula to solve for

a .

\frac{a}{b} = \frac{p}{1 0 0}

SubstituteII

$b = 35$ , $p = 75$

\frac{a}{3 5} = \frac{7 5}{1 0 0}

ReduceFrac

$\frac{a}{b} = \frac{a / 2 5}{b / 2 5}$

\frac{a}{3 5} = \frac{3}{4}

MultEqn

$LHS \cdot 35 = RHS \cdot 35$

\frac{a}{3 5} \cdot 35 = \frac{3}{4} \cdot 35

FracMultDenomToNumber

$\frac{a}{3 5} \cdot 35 = a$

a = \frac{3}{4} \cdot 35

MoveRightFacToNum

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

a = \frac{3 \cdot 3 5}{4}

Multiply

a = \frac{1 0 5}{4}

CalcQuot

Calculate quotient

a = 26.25

Since Kara cannot get a fraction of a question correct, she has to answer

27

questions correctly to score at least a

75 % .