Chris puts one tenth of each paycheck into savings. Her current paycheck is $200. She decides to also put into savings, any amount she earns over $200. The expression below represents the percent of her paycheck that Chris saves when she makes x dollars more than her current paycheck.
100(x+20)x+200100(x+20)x+200
Drag and drop the expressions into the boxes to identify their meaning.
Original Ratio of Saved to Total Money per Paycheck Final Ratio of Saved to Total Money per Paycheck Final Amount Saved per Paycheck
Original Ratio of Saved to Total Money per Paycheck: 1/10 (or 10%)
Final Ratio of Saved to Total Money per Paycheck: (x+20)/(x+200)
Final Amount Saved per Paycheck: (x+20)/(x+200) * (x+200) = (x+20) dollars
Explanation:
- The original ratio of saved to total money per paycheck is given as 1/10, which means Chris saves 1/10 or 10% of her paycheck.
- However, if she makes an amount x dollars more than her current paycheck, she decides to save any amount earned over $200. This means the additional amount she saves will be the difference between x and 200.
- The final ratio of saved to total money per paycheck is expressed as (x+20)/(x+200). The numerator (x+20) represents the total amount saved (starting from $200 and including the additional amount saved) and the denominator (x+200) represents the total money per paycheck (starting from $200 and including the additional amount earned).
- Therefore, the final amount saved per paycheck is obtained by multiplying the final ratio by the total money per paycheck, i.e., (x+20)/(x+200) * (x+200) which simplifies to (x+20) dollars.
Original Ratio of Saved to Total Money per Paycheck: $\frac{100}{x+200}$
Final Ratio of Saved to Total Money per Paycheck: $\frac{100}{x+20+x+200}$ or $\frac{100}{2x+220}$
Final Amount Saved per Paycheck: $(\frac{100}{2x+220})(x+20+x+200)$ or $(\frac{100}{2x+220})(2x+220)$