Question

algebra & ratios
11/23/24
solve each proportion. use cross products.
day 7

1. $\frac{1}{4} = \frac{x}{8}$

2 $\frac{20}{30} = \frac{5}{d}$

1. $\frac{18}{24} = \frac{12}{l}$
2. $\frac{80}{m} = \frac{48}{20}$
3. $\frac{5}{5} = \frac{5n}{5}$
4. $\frac{15}{45} = \frac{3}{t}$
5. $\frac{18}{v} = \frac{3.6}{2.8}$
6. $\frac{8}{z} = \frac{5}{2}$
7. $\frac{8}{6} = \frac{s}{27}$
8. $\frac{144}{6} = \frac{6c}{6}$
9. $\frac{r}{3} = \frac{8}{8}$
10. $\frac{36}{12} = \frac{b}{6}$
11. $\frac{0.14}{0.07} = \frac{k}{15}$
12. $\frac{6}{w} = \frac{6}{4}$
13. $\frac{4}{5} = \frac{f}{5}$
14. $\frac{16}{48} = \frac{h}{50}$

solve each inequality and graph its solution.

1. $15 × x ≤ 15$
2. $h ÷ 6 < -12$
3. $-10a < -70$
4. $n ÷ 2 ≥ 2$

Explanation:

Step1: Cross-multiply to solve for $x$

$1 \times 8 = 4 \times x$
$8 = 4x$
$x = \frac{8}{4} = 2$

Step2: Cross-multiply to solve for $d$

$20 \times d = 30 \times 5$
$20d = 150$
$d = \frac{150}{20} = 7.5$

Step3: Cross-multiply to solve for $l$

$18 \times l = 24 \times 12$
$18l = 288$
$l = \frac{288}{18} = 16$

Step4: Cross-multiply to solve for $m$

$80 \times 20 = m \times 48$
$1600 = 48m$
$m = \frac{1600}{48} = \frac{100}{3} \approx 33.33$

Step5: Cross-multiply to solve for $n$

$5 \times 5 = 5 \times 5n$
$25 = 25n$
$n = \frac{25}{25} = 1$

Step6: Cross-multiply to solve for $t$

$15 \times t = 45 \times 3$
$15t = 135$
$t = \frac{135}{15} = 9$

Step7: Cross-multiply to solve for $v$

$1.8 \times 2.8 = v \times 3.6$
$5.04 = 3.6v$
$v = \frac{5.04}{3.6} = 1.4$

Step8: Cross-multiply to solve for $z$

$8 \times 2 = z \times 5$
$16 = 5z$
$z = \frac{16}{5} = 3.2$

Step9: Cross-multiply to solve for $s$

$8 \times 27 = 6 \times s$
$216 = 6s$
$s = \frac{216}{6} = 36$

Step10: Cross-multiply to solve for $c$

$144 \times 6 = 6 \times 6c$
$864 = 36c$
$c = \frac{864}{36} = 24$

Step11: Cross-multiply to solve for $r$

$r \times 8 = 3 \times 8$
$8r = 24$
$r = \frac{24}{8} = 3$

Step12: Cross-multiply to solve for $b$

$36 \times 6 = 12 \times b$
$216 = 12b$
$b = \frac{216}{12} = 18$

Step13: Cross-multiply to solve for $k$

$0.14 \times 1.5 = 0.07 \times k$
$0.21 = 0.07k$
$k = \frac{0.21}{0.07} = 3$

Step14: Cross-multiply to solve for $w$

$6 \times 4 = w \times 6$
$24 = 6w$
$w = \frac{24}{6} = 4$

Step15: Cross-multiply to solve for $f$

$4 \times 5 = 5 \times f$
$20 = 5f$
$f = \frac{20}{5} = 4$

Step16: Cross-multiply to solve for $h$

$16 \times 50 = 48 \times h$
$800 = 48h$
$h = \frac{800}{48} = \frac{50}{3} \approx 16.67$

Step17: Isolate $x$

$15x \leq 15$
$x \leq \frac{15}{15}$
$x \leq 1$
Graph: Closed circle at 1, arrow left to -3.

Step18: Isolate $h$

$h \div 6 < -12$
$h < -12 \times 6$
$h < -72$
Graph: Open circle at -72, arrow left to -80.

Step19: Isolate $a$ (reverse inequality)

$-10a < -70$
$a > \frac{-70}{-10}$
$a > 7$
Graph: Open circle at 7, arrow right to 10.

Step20: Isolate $n$

$n \div 2 \geq 2$
$n \geq 2 \times 2$
$n \geq 4$
Graph: Closed circle at 4, arrow right to 9.

Answer:

1. $x=2$
2. $d=7.5$
3. $l=16$
4. $m=\frac{100}{3}$
5. $n=1$
6. $t=9$
7. $v=1.4$
8. $z=3.2$
9. $s=36$
10. $c=24$
11. $r=3$
12. $b=18$
13. $k=3$
14. $w=4$
15. $f=4$
16. $h=\frac{50}{3}$
17. $x \leq 1$ (graph: closed circle at 1, left arrow)
18. $h < -72$ (graph: open circle at -72, left arrow)
19. $a > 7$ (graph: open circle at 7, right arrow)
20. $n \geq 4$ (graph: closed circle at 4, right arrow)