Multi-Step Problems with Percent

Multi-Step Problems with Percent exercise

• Explain the meaning of $45~\%$ discount for the penguin skis.

  Hints

  Discount is a reduction of the usual price.

  For example, a discount of $30~\%$ off the original price of an item that costs $100~\$$, will result in the discounted price of $70~\$$.

  Remember: percent means dividing by $100$:

  $45~\%=\frac{45}{100}$

  Solution

  Penguin skis normally cost $225$ fish dollars, but the yeti only has $150$ fish dollars. It's her lucky day, there's a special offer for today: $45~\%$ off the regular price of the rental.

  What does this mean for our yeti? First of all, we know that the discounted price is lower than the original price. But how much lower?

  To find out, we can calculate $45~\%$ of $225$, and then subtract the outcome from $225$.

  An alternate strategy: we can directly calculate $100~\%-45~\%= 55~\%$ of $225$ fish dollars. So, to calculate the new price, we can simply multiply the original price by $55~\%$.

• Calculate the price the yeti has to pay for the new penguin skis.

  Hints

  Because the discount will be subtracted, the offer price will be lower than the original price.

  Multiplying by $45~\%$ is the same as multiplying by $\frac{45}{100}$.

  To multiply an integer with a fraction, first multiply the integer by the numerator then divide the product by the denominator.

  Solution

  The full priced rental fee for penguin skis is $225$ fish dollars.

  To calculate the price with the discount and tax:

  Calculate the discount of $45~\%$ by multiplying the original price by the percentage: $225\times 45~\%=101.25$

  Then subtract the discount from the original price: $225-101.25=123.75$

  This difference is the reduced price, but we still need to calculate the tax:

  Multiply the tax rate by the reduced price: $123.75\times 8~\%=9.90$

  Finally, we add the amount of tax to the reduced price: $123.75+9.90=133.65$

  Yeah! We know that Betty the yeti has enough money to pay for the skis. She can rent the skis and start skiing!

• Examine the different rental fees for penguin skis.

  Hints

  Keep in mind that $30~\%$ means $\frac{30}{100}$.

  You can use a shortcut to calculate the discounted price and the tax. Take a look at the following example:

  The original price is $200$, and there is a special offer of $30~\%$ discount.

  $200\times (100~\%-30~\%)=200\times 70~\%=140$

  Notice, you can skip a step and still get the same answer.

  Solution

  For each shop, let's calculate the rental fee for the penguin skis and the percent discount.

  1. The lowest price we can get is from the blue shop: $180\times (100~\%-30~\%)=180\times 70~\%=126$.
  2. The green shop offers skis for $130$ without any discount.
  3. The red shop offers skis for $230\times (100~\%-40~\%)=230\times 60~\%=138$.
  4. In the violet shop, you have to pay $160\times (100~\%-10~\%)=160\times 90~\%=144$.
  5. The yellow shop has an offer of $240\times (100~\%-35~\%)=240\times 65~\%=156$.

  You can see that it's very important to understand how to calculate with percent. You can save a lot of money!

• Calculate the check including the tip.

  Hints

  Before you can calculate the discount, first add the cost of the burger and the water .

  You can either calculate $5\times 10~\%$ and subtract the result from $5$ or calculate $5\times (100~\%-10~\%)=5\times 90~\%$.

  The result is the same.

  In a similar manner you can either calculate the $20~\%$ tip first and add it to the previous amount or multiply the amount by $120~\%$.

  Solution

  After finishing her delicious meal, Susan wants to pay:

  The total price is: $3.75+1.25=5$. Now she can calculate the discount and subtract it:

  $5\times 10~\%=0.5$

  Susan has to pay $5-0.5=4.5$.

  But, Susan wants to give a $20~\%$ tip, so to calculate the tip, she multiplies the new price by $20~\%$:

  $4.5\times 20~\%=0.90$

  Susan's bill including the tip is $4.5+0.9=5.40$ in total.

• Change $45~\%$ into a fraction and a decimal.

  Hints

  Remember: percent means parts per hundred.

  Notice the result is to shift the decimal point to the left. For example:

  $\large{\frac{3}{100}}=0.03$

  Solution

  For calculating with percent, it's important that you understand the meaning of percentage.

  The actual meaning of percent is per hundred. $45~\%$ can be written as a fraction or as a decimal number. In fraction form, it is easy to recognize the meaning of per hundred:

  $45~\%=\frac{45}{100}=0.45$

• Evaluate the final check the Yetis and the Penguins have to pay.

  Hints

  Without the discount and the tip, the yetis would pay $64$ dollars.

  They get a discount of $12.80$ dollars.

  Solution

  First, let's have a look at the yetis. We calculate their total check by adding the prices for their lemonades and chips:

  $15\times 3+5\times 3.8=64$

  The discount can be calculated by:

  $64\times 20~\%=12.80$

  This amount has to be subtracted from the original price:

  $64-12.80=51.20$

  Now we can calculate the tip:

  $51.20\times 15~\%=7.68\approx 7.70$

  And add it to the bill:

  $51.20+7.70=58.90$.

  Therefore the yetis have to pay $\$~58.90$ in total.

  $~$

  Now we take a look at the penguins. Their total check is:

  $12\times 4.5=54$

  The discount can be calculated as follows:

  $54\times 35~\%=18.90$

  Subtracting the discount leads to:

  $54-18.90=35.10$

  Now we only need to add the tip $35.10\times20~\%=7.02\approx 7.00$

  So we get $35.10+7.00=42.10$.

  The penguins have to pay $\$~42.10$ in total.