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Quiz 6
1.) Solve for $x$:
$$-3x+2=-7.$$
Solution: First add $-2$ to both sides (or "subtract $2$ from both sides") to get
$$-3x = -9.$$
Now multiply both sides by $-\dfrac{1}{3}$ (or "divide both sides by $-3$") to get
$$x=\dfrac{-9}{-3} = 3.$$
2.) The relationship between the rate of travel (denoted $r$) the distance travelled (denoted $d$), and the time it took to travel (denoted $t$) is
$$r = \dfrac{d}{t}.$$
If you travelled $200$ miles in $3$ hours, at what rate were you travelling?
Solution: The given information is $d=200$ miles and $t=3$ hours. Plug this information into the equation to get
$$r = \dfrac{200 \hspace{2pt} \mathrm{miles}}{3 \hspace{2pt} \mathrm{hours}}=\dfrac{200}{3} \dfrac{\mathrm{miles}}{\mathrm{hour}}.$$
Note: you are welcome to express $\dfrac{200}{3}$ as a decimal and get $66.66...$ miles/hour.
3.) What is $4\%$ of $57$ (as a decimal)?
Solution: Recall how to translate this into an equation: "what" becomes the variable "x", "is" becomes "=", "%" becomes "$\dfrac{1}{100}$", and "of" becomes multiplication. Therefore we get
$$x = \dfrac{4}{100} \cdot 57.$$
Now just use arithmetic to get a deicmal answer as follows:
$$x =\dfrac{4}{100} \cdot 57 = \dfrac{228}{100} = 2.28.$$
