Question

what is the area of the rectangle? mr. hoskins uses automatic bill pay to pay his bills each month. the cable bill deducts $66.45 every month. how much will the cable bill deductions be in total for the year? a scuba diver is 4\frac{2}{3} feet below the surface of the water. she then dives another 2\frac{1}{2} feet. how far below the surface of the water is the scuba diver?

Explanation:

Step1: Convert mixed - numbers to improper fractions for rectangle area

$2\frac{1}{5}=\frac{2\times5 + 1}{5}=\frac{11}{5}$ and $3\frac{1}{8}=\frac{3\times8+1}{8}=\frac{25}{8}$

Step2: Use rectangle area formula $A = l\times w$

$A=\frac{11}{5}\times\frac{25}{8}=\frac{11\times25}{5\times8}=\frac{275}{40}=\frac{55}{8}=6\frac{7}{8}$ square yards

Step3: Calculate annual cable bill deduction

Monthly deduction is $66.45$. There are 12 months in a year. So total deduction $=66.45\times12 = 797.4$ dollars

Step4: Add depths for scuba - diver problem

$4\frac{2}{3}=\frac{4\times3 + 2}{3}=\frac{14}{3}$ and $2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{5}{2}$
Find a common denominator, which is 6. $\frac{14}{3}=\frac{14\times2}{3\times2}=\frac{28}{6}$ and $\frac{5}{2}=\frac{5\times3}{2\times3}=\frac{15}{6}$
$\frac{28}{6}+\frac{15}{6}=\frac{28 + 15}{6}=\frac{43}{6}=7\frac{1}{6}$ feet

Answer:

D. $6\frac{7}{8}$ square yards
E. $797.4$ dollars
F. $7\frac{1}{6}$ feet