Question

isabella bought a skirt at the local clothing store. after paying a 5% tax, her total was $68.25. what was the cost of the skirt before tax? a) $34.12 b) $50 c) $64.84 d) $65 e) $71.66. if $\frac{x}{8}=\frac{10}{2x}$, then what is the value of $x^{2}$? a) $2sqrt{10}$ b) $10sqrt{2}$ c) 40 d) 60 e) 80. 14. for a specific chemistry class at a school, there are only sophomores and juniors. if the ratio of sophomores to juniors in this chemistry class is 5:7, what percent of the students are juniors? a) 58% b) 42% c) 50% d) 71% e) 80%. 15. an automatic wood saw can cut forty pieces of wood in one hour. at this rate, how many pieces of wood can it cut in fifteen minutes? a) 5 b) 10 c) 15 d) 20 e) 25

Explanation:

Question 1

Step1: Set up an equation

Let the cost of the skirt before tax be $x$. The tax is 5% of $x$, so the total cost is $x + 0.05x=1.05x$. We know that $1.05x = 68.25$.

Step2: Solve for $x$

Divide both sides of the equation $1.05x = 68.25$ by 1.05: $x=\frac{68.25}{1.05}=65$.

Step1: Cross - multiply

Given $\frac{x}{8}=\frac{10}{2x}$, cross - multiplying gives $x\times(2x)=8\times10$.

Step2: Simplify the equation

$2x^{2}=80$.

Step3: Solve for $x^{2}$

Divide both sides of the equation $2x^{2}=80$ by 2, we get $x^{2} = 40$.

Step1: Calculate the total number of parts

The ratio of sophomores to juniors is 5:7, so the total number of parts is $5 + 7=12$.

Step2: Find the percentage of juniors

The percentage of juniors is $\frac{7}{12}\times100\%\approx58.33\%\approx58\%$.

Answer:

D. $65$

Question 2