Tax and tip word problems

Google Classroom

Problem

Handsome Jack is buying a pony made of diamonds. The price of the pony is $P$P dollars, and Jack also has to pay a $25\%$25, percent diamond pony tax.

Which of the following expressions could represent how much Jack pays in total for the pony?

Choose 2 answers:

Choose 2 answers:

• (Choice A, Incorrect)

  INCORRECT

  $P+\dfrac{1}{4}$P, plus, start fraction, 1, divided by, 4, end fraction

  $P$P represents the price of the pony, and $\dfrac{1}{4}$start fraction, 1, divided by, 4, end fraction represents the tax rate. We can only add like units, so adding an amount of money to a rate would not be meaningful.
• (Choice B, Checked, Correct)

  CORRECT (SELECTED)

  $P+{0.25} P$P, plus, 0, point, 25, P
• (Choice C, Incorrect)

  INCORRECT

  $\left(P+\dfrac{1}{4}\right)P$left parenthesis, P, plus, start fraction, 1, divided by, 4, end fraction, right parenthesis, P

  $P$P represents the price of the pony, and $\dfrac{1}{4}$start fraction, 1, divided by, 4, end fraction represents the tax rate. We can only add like units, so adding an amount of money to a rate would not be meaningful.
• (Choice D, Checked, Correct)

  CORRECT (SELECTED)

  $\dfrac{5}{4}P$start fraction, 5, divided by, 4, end fraction, P
• (Choice E, Incorrect)

  INCORRECT

  $0.25P$0, point, 25, P

  This is the amount of the tax Jack pays.

Hint #11 / 5

The tax is $25\%$25, percent of the price $P$P of the pony.

So Jack has to pay $\greenD{25\%\cdot P}$start color #1fab54, 25, percent, dot, P, end color #1fab54 dollars of tax.

Hint #22 / 5

That means that he pays a total of $\maroonD{P}+\greenD{25\%\cdot P}$start color #ca337c, P, end color #ca337c, plus, start color #1fab54, 25, percent, dot, P, end color #1fab54 for the pony.

Hint #33 / 5

Because $25\%$25, percent means $25$25 per hundred, we can write it in equivalent forms.

$\begin{aligned} 25\%&=\dfrac{25}{100}\\\\ &=\dfrac{1}{4}\\\\ &=0.25 \end{aligned}$

Hint #44 / 5

Let's find equivalent ways of writing the amount Jack pays in total for the diamond pony.

$\begin{aligned} P+\blueD{25\%}\cdot P&=P+\blueD{0.25} P\\\\ &=P+\blueD{\dfrac{1}{4}}\cdot P\\\\ &=\left(1+\dfrac{1}{4}\right)P\\\\ &=\dfrac{5}{4}P \end{aligned}$

Hint #55 / 5

The expressions $P+{0.25} P$P, plus, 0, point, 25, P and $\dfrac{5}{4}P$start fraction, 5, divided by, 4, end fraction, P each could represent how much Jack pays in total for the pony.