name date double discounts complete this chart original price sale discount sale price additional 20% off…
name date double discounts complete this chart original price sale discount sale price additional 20% off new price % savings off 1. $29.99 15% $4.50 $25.49 $5.10 $20.39 32% 2. $179.99 25% 3. $489.99 50% 4. $74.99 30% 5. $159.98 $79.99 6. 75% $18.75 7. $15.79 $6.32 8. what do you notice about the percent of savings in the examples above when you have a double sale? what do most people think they are getting for a savings? 9. which is a better deal on a $50 item: 45% off original price or 30% off and additional 20% off at the register?
Answer
Explanation:
Step1: Calculate discount for $179.99 item
Discount = $179.99\times0.25=$44.9975\approx$45.00$
Step2: Calculate sale price for $179.99 item
Sale price = $179.99 - 45.00=$134.99$
Step3: Calculate additional 20% - off amount for $179.99 item
Additional discount = $134.99\times0.2=$26.998\approx$27.00$
Step4: Calculate new price for $179.99 item
New price = $134.99 - 27.00=$107.99$
Step5: Calculate percent - savings for $179.99 item
Percent savings = $\frac{179.99 - 107.99}{179.99}\times100%\approx40%$
Step6: Calculate discount for $489.99 item
Discount = $489.99\times0.5=$244.995\approx$245.00$
Step7: Calculate sale price for $489.99 item
Sale price = $489.99 - 245.00=$244.99$
Step8: Calculate additional 20% - off amount for $489.99 item
Additional discount = $244.99\times0.2=$48.998\approx$49.00$
Step9: Calculate new price for $489.99 item
New price = $244.99 - 49.00=$195.99$
Step10: Calculate percent - savings for $489.99 item
Percent savings = $\frac{489.99 - 195.99}{489.99}\times100%\approx60%$
Step11: Calculate discount for $74.99 item
Discount = $74.99\times0.3=$22.497\approx$22.50$
Step12: Calculate sale price for $74.99 item
Sale price = $74.99 - 22.50=$52.49$
Step13: Calculate additional 20% - off amount for $74.99 item
Additional discount = $52.49\times0.2=$10.498\approx$10.50$
Step14: Calculate new price for $74.99 item
New price = $52.49 - 10.50=$41.99$
Step15: Calculate percent - savings for $74.99 item
Percent savings = $\frac{74.99 - 41.99}{74.99}\times100%\approx44%$
Step16: Calculate sale percentage for $159.98 item
Since sale price is $79.99$, sale percentage = $\frac{159.98 - 79.99}{159.98}\times100% = 50%$ Discount = $159.98\times0.5=$79.99$ Additional discount = $79.99\times0.2=$15.998\approx$16.00$ New price = $79.99 - 16.00=$63.99$ Percent savings = $\frac{159.98 - 63.99}{159.98}\times100%\approx60%$
Step17: Calculate original price for item with 75% discount and $18.75 discount
Let the original price be $x$. Then $0.75x = 18.75$, so $x=\frac{18.75}{0.75}=$25.00$ Sale price = $25.00 - 18.75=$6.25$ Additional discount = $6.25\times0.2=$1.25$ New price = $6.25 - 1.25=$5.00$ Percent savings = $\frac{25.00 - 5.00}{25.00}\times100% = 80%$
Step18: Calculate sale percentage for $15.79 item
Since discount is $6.32$, sale percentage = $\frac{6.32}{15.79}\times100%\approx40%$ Sale price = $15.79 - 6.32=$9.47$ Additional discount = $9.47\times0.2=$1.894\approx$1.90$ New price = $9.47 - 1.90=$7.57$ Percent savings = $\frac{15.79 - 7.57}{15.79}\times100%\approx52%$
Step19: Analyze percent - savings for double - sale
Most people might think that a double - sale of $30%$ off and then $20%$ off is equivalent to a $50%$ off. But in reality, the combined discount is less than the sum of the individual discounts. For example, if the original price is $P$, after a $30%$ off, the price is $P_1=(1 - 0.3)P = 0.7P$. Then after a $20%$ off on $P_1$, the new price is $P_2=(1 - 0.2)\times0.7P=0.56P$, so the total discount is $1 - 0.56 = 0.44$ or $44%$, not $50%$.
Step20: Compare deals for $50 item
For $45%$ off on a $50$ item: Discount = $50\times0.45=$22.50$ New price = $50 - 22.50=$27.50$
For $30%$ off first: First - stage discount = $50\times0.3=$15.00$ First - stage price = $50 - 15.00=$35.00$ Second - stage discount (20% off $35$) = $35\times0.2=$7.00$ New price = $35.00 - 7.00=$28.00$
The $45%$ off deal is better.
Answer:
| Original Price | Sale | Discount | Sale Price | Additional 20% Off | New Price | % Savings Off |
|---|---|---|---|---|---|---|
| $29.99$ | $15%$ | $4.50$ | $25.49$ | $5.10$ | $20.39$ | $32%$ |
| $179.99$ | $25%$ | $45.00$ | $134.99$ | $27.00$ | $107.99$ | $40%$ |
| $489.99$ | $50%$ | $245.00$ | $244.99$ | $49.00$ | $195.99$ | $60%$ |
| $74.99$ | $30%$ | $22.50$ | $52.49$ | $10.50$ | $41.99$ | $44%$ |
| $159.98$ | $50%$ | $79.99$ | $79.99$ | $16.00$ | $63.99$ | $60%$ |
| $25.00$ | $75%$ | $18.75$ | $6.25$ | $1.25$ | $5.00$ | $80%$ |
| $15.79$ | $40%$ | $6.32$ | $9.47$ | $1.90$ | $7.57$ | $52%$ |
| 8. Most people over - estimate the total discount. The combined discount is less than the sum of individual discounts. | ||||||
| 9. $45%$ off original price is a better deal. |