Question

1. the oligarchs were in control, although they comprised only 0.0032 of the total population. if there were 1280 oligarchs, what was the total population?
2. the boys believed that temerity was a desirable attribute, so the number of boys who were temerarious increased 132 percent in only one month. if the temerarious now number 9280, how many boys were temerarious last month?
3. the chemical formula for sodium hydroxide is naoh. what is the weight of the sodium (na) in 320 grams of sodium hydroxide (na, 23; o, 16; h, 1)?
4. twenty - three percent of the mixture was cadmium. if the total weight of the mixture was 3000 grams, what was the weight of the other constituents of the mixture?
5. connie was 20 miles ahead of larry when he started after her. if he caught her in 5 hours and traveled twice as fast as she traveled, how far did he have to go to catch her?

Explanation:

Problem 1

Step1: Define variables and formula

Let total population = $P$. We know $0.0032P = 1280$, so $P=\frac{1280}{0.0032}$

Step2: Calculate total population

$\frac{1280}{0.0032}=400000$

Problem 2

Step1: Define last month's count

Let last month's count = $x$. A 132% increase means current count = $x + 1.32x = 2.32x$

Step2: Solve for $x$

$x=\frac{9280}{2.32}=4000$

Problem 3

Step1: Calculate molar mass of NaOH

Molar mass = $23 + 16 + 1 = 40$ g/mol

Step2: Find mass fraction of Na

Mass fraction of Na = $\frac{23}{40}$

Step3: Calculate Na mass in 320g

Mass of Na = $320 \times \frac{23}{40}=184$ grams

Problem 4

Step1: Find percentage of other constituents

Other constituents % = $100\% - 23\% = 77\% = 0.77$

Step2: Calculate weight of other constituents

Weight = $3000 \times 0.77=2310$ grams

Problem 5

Step1: Define speeds and distance

Let Connie's speed = $v$, Larry's speed = $2v$. Relative speed = $2v - v = v$

Step2: Find Connie's speed

Larry closes 20 miles in 5 hours, so $v=\frac{20}{5}=4$ mph. Larry's speed = $8$ mph

Step3: Calculate Larry's travel distance

Distance = $8 \times 5 = 40$ miles

Answer:

1. 400000
2. 4000
3. 184 grams
4. 2310 grams
5. 40 miles