Leila is buying a dinosaur model. The price of the model is $x$ dollars, and she also has to pay a $7 \%$ tax. $\newline$ Which of the following expressions could represent how much Leila pays in total for the model? $\newline$ Choose $2$ answers: $\newline$ (A) $\frac{107}{100} x$ $\newline$ B $0.7 x+x$ $\newline$ c $1.07 x$ $\newline$ D $x+\frac{7}{10} x$ $\newline$ E $1.7 x$

Full solution

Q. Leila is buying a dinosaur model. The price of the model is

x

dollars, and she also has to pay a

7 \%

tax.

\newline

Which of the following expressions could represent how much Leila pays in total for the model?

\newline

Choose

2

answers:

\newline

(A)

\frac{107}{100} x

\newline

0.7 x+x

\newline

1.07 x

\newline

x+\frac{7}{10} x

\newline

1.7 x

Calculate Tax Amount: Leila is buying a dinosaur model for $x$ dollars with an additional $7\%$ tax. To find the total cost, we need to calculate the tax amount and add it to the original price. The tax can be calculated as $7\%$ of $x$ , which is $0.07$ times $x$ .
Find Total Cost: The total cost is the original price plus the tax. So, we add $x$ and $0.07x$ together to get the total cost. This can be expressed as $x + 0.07x$ .
Combine Like Terms: Simplify the expression $x + 0.07x$ by combining like terms. This gives us $1x + 0.07x$ , which equals $1.07x$ .
Check Given Options: Now, let's check the given options to see which ones match our simplified expression of $1.07x$ . Option (A) is $(107/100)x$ , which simplifies to $1.07x$ . Option (C) is directly given as $1.07x$ . Both of these options are correct representations of the total cost.
Incorrect Option (B): Option (B) is $0.7x + x$ , which simplifies to $1.7x$ . This is incorrect because it represents a $70\%$ tax, not a $7\%$ tax.
Incorrect Option (D): Option (D) is $x + \left(\frac{7}{10}\right)x$ , which simplifies to $1x + 0.7x$ , or $1.7x$ . This is also incorrect for the same reason as option (B).
Incorrect Option (E: Option (E) is $1.7x$ , which is incorrect as it represents a $70\%$ increase, not a $7\%$ tax.