Percents: Percent Translation

If Mark saves 50% more than Sally every month, Sally's annual savings are approximately what percent of Mark's annual savings?

Incorrect. [[snippet]]

Correct. [[snippet]] It is always better to start with the smallest variable, so make Sally's monthly savings the invisible variable. When the problem asks about percents, use 100. So if Sally saves $100 per month, Mark saves 50% more (i.e., $150). Now pause for a moment. Did you multiply Sally's and Mark's savings by 12 (months)?

Incorrect. [[snippet]]

Incorrect. [[snippet]]

Incorrect. [[snippet]]

There's really no need to multiply Mark's or Sally's savings. If Mark saves 50% more than Sally does every month, it is the same for a whole year's savings. Save yourself the trouble and work with smaller numbers. The question is actually a percent translation sentence. And so, {color:purple}"Sally's annual savings are approximately what percent of Mark's annual savings?"{/color} translates into >$$\displaystyle 100=\frac{x}{100}\cdot150$$. Reduce $$\frac{150}{100}$$ by 50 to $$\frac{3}{2}$$ and solve for $$x$$: >$$\displaystyle 100 = \frac{3x}{2}$$ >$$\displaystyle 200 = 3x \hspace{0.3in}$$ [Multiply by 2] >$$\displaystyle \frac{200}{3} = x \hspace{0.4in}$$ [Divide by 3] >$$\displaystyle x=\frac{200}{3} \approx 66.7$$.

25%

33%

50%

67%

75%

Of course I did. How else can I answer the question?

No, I didn't. There's no need.