Multi-Step Problems with Percent02:43 minutes

Video Transcript

TranscriptMulti-Step Problems with Percent

There is a big ski event today at the South Pole. To show off her mad skiing skills, a pretty Yeti named Betty, wants to rent some new penguin skis, but Betty has a budget, and she doesn’t want to spend more than one hundred fifty fish dollars on the rental. Does she have enough money to rent the skis? Let's find out.

Solving multi-step Problems with Percents

The regular price to rent penguin skis is 225 fish dollars, but for today only, there is a 45% discount. Sales tax is 8% of the original rental price. Let's calculate the total cost of the rental, including the 45% discount and the 8% sales tax.

1. First, let's determine the new price of the rental by calculating the discount: 225 · 45% = 101.25. Remember: Percent means you have to divide by 100.
2. Next, subtract the discount from the full price: 225 − 101.25 i= 123.75.
3. Since we gotta pay the tax man, calculate the 8% tax: 123.75 · 8% = 9.90.
4. Taxes increase the price of things, so add the tax to determine the total cost: 123.75 + 9.90 = 133.65.

Betty must pay 133.65, in fish currency, to rent the skis.

Easier way to solve the multi-step Problem with Percents

That's a lot of calculations. You may be thinking… is there an easier way? You betcha! How 'bout I show you a shortcut?

The full price is 225, which is 100%. So, since 100% minus the 45% discount is equal to 55%, we can save a step by calculating 55% of the full price to determine the new price: 225 · 55% = 123.75.

Don't forget to include the sales tax: 100% + 8% = 108%. Multiply the new price times 108%. The total price is 133.65 in fish dollars, of course.

And best of all, Pretty Betty the Yeti has enough money to rent the penguin skis. She is super excited to hit the slopes! But the penguins, they're not so sure.

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Proportion and Percents (7 Videos)

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

Tipps

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$100$:$45~\%=\frac{45}{100}$Lösung 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$55~\%$. • Change$45~\%$into a fraction and a decimal. Tipps Remember: percent means parts per hundred. Notice the result is to shift the decimal point to the left. For example:$\large{\frac{3}{100}}=0.03$Lösung 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:$45~\%=\frac{45}{100}=0.45$• Calculate the price the yeti has to pay for the new penguin skis. Tipps 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. Lösung 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! • Evaluate the final check the Yetis and the Penguins have to pay. Tipps Without the discount and the tip, the yetis would pay$64$dollars. They get a discount of$12.80$dollars. Lösung 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:

$54\times 35~\%=18.90$

$54-18.90=35.10$
Now we only need to add the tip $35.10\times20~\%=7.02\approx 7.00$
So we get $35.10+7.00=42.10$.