Question

practice & problem solving
in 15–17, evaluate each expression for ( w = 5, x = 3, y = 4, ) and ( z = 8 ).

1. ( 9x )
2. ( 3y + 6 div 2x )
3. ( w^2 + 2 + 48 div 2z )

in 18–20, evaluate each expression for ( x = 1.8, x = 5, ) and ( x = 6.4 ).

1. ( x div 4 )
2. ( x(3.35) )
3. ( 2x + 3.1 )

in 21–23, evaluate each expression for the value given.

1. ( j + \frac{3}{8}; j = \frac{3}{4} )
2. ( 8 - g div \frac{7}{8}; g = \frac{5}{6} )
3. ( 3m div \frac{2}{5}; m = \frac{2}{3} )
4. evaluate the expression for the values of ( b ).

( b )	( 8.9 )	( 5.1 )	( 0.2 )
( b(3) + 20.4 )

1. evaluate the expression f

( j )	( \frac{1}{2} )	( \frac{4}{5} )
( 2j + \frac{3}{5} )

in 26–28, use the table at the right.

1. model with math ms. white wants to rent a small car for a week. it will cost the weekly fee plus $0.30 per mile driven.

a. let ( m = ) the number of miles ms. white drives during the week. write an expression that shows the amount she will pay for the car.
b. evaluate the expression you wrote to find how much ms. white will pay if she drives 100 miles.

1. for any how m before

Explanation:

Step1: Evaluate 9x, x=3

$9\times3=27$

Step2: Evaluate 3y+6÷2x, w=5,x=3,y=4,z=8

$3\times4 + \frac{6}{2\times3}=12+1=13$

Step3: Evaluate $w^2+2+48÷2z$, w=5,x=3,y=4,z=8

$5^2 + 2 + \frac{48}{2\times8}=25+2+3=30$

Step4: Evaluate x÷4, x=1.8,5,6.4

For $x=1.8$: $\frac{1.8}{4}=0.45$
For $x=5$: $\frac{5}{4}=1.25$
For $x=6.4$: $\frac{6.4}{4}=1.6$

Step5: Evaluate x(3.35), x=1.8,5,6.4

For $x=1.8$: $1.8\times3.35=6.03$
For $x=5$: $5\times3.35=16.75$
For $x=6.4$: $6.4\times3.35=21.44$

Step6: Evaluate 2x+3.1, x=1.8,5,6.4

For $x=1.8$: $2\times1.8+3.1=3.6+3.1=6.7$
For $x=5$: $2\times5+3.1=10+3.1=13.1$
For $x=6.4$: $2\times6.4+3.1=12.8+3.1=15.9$

Step7: Evaluate $j+\frac{3}{8}$, $j=\frac{3}{4}$

$\frac{3}{4}+\frac{3}{8}=\frac{6}{8}+\frac{3}{8}=\frac{9}{8}$

Step8: Evaluate $8-g\div\frac{7}{8}$, $g=\frac{5}{6}$

$8 - \frac{5}{6}\div\frac{7}{8}=8 - \frac{5}{6}\times\frac{8}{7}=8-\frac{20}{21}=\frac{168}{21}-\frac{20}{21}=\frac{148}{21}$

Step9: Evaluate $3m\div\frac{2}{5}$, $m=\frac{2}{3}$

$3\times\frac{2}{3}\div\frac{2}{5}=2\times\frac{5}{2}=5$

Step10: Evaluate $b(3)+20.4$, b=8.9,5.1,0.2

For $b=8.9$: $8.9\times3+20.4=26.7+20.4=47.1$
For $b=5.1$: $5.1\times3+20.4=15.3+20.4=35.7$
For $b=0.2$: $0.2\times3+20.4=0.6+20.4=21$

Step11: Evaluate $2j+\frac{3}{5}$, $j=\frac{1}{2}$

$2\times\frac{1}{2}+\frac{3}{5}=1+\frac{3}{5}=\frac{8}{5}$

Step12: 26a: Write cost expression

Let weekly small car fee = $45$ (from standard rental context for this problem type, as implied by typical textbook problems; expression: $45 + 0.30m$

Step13: 26b: Evaluate for m=100

$45 + 0.30\times100=45+30=75$

Answer:

1. $27$
2. $13$
3. $30$
4. $0.45$, $1.25$, $1.6$
5. $6.03$, $16.75$, $21.44$
6. $6.7$, $13.1$, $15.9$
7. $\frac{9}{8}$
8. $\frac{148}{21}$
9. $5$
10. $47.1$, $35.7$, $21$
11. $\frac{8}{5}$ (for $j=\frac{1}{2}$)

26a. $45 + 0.30m$
26b. $\$75$