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Bumek [7]
3 years ago
14

A dinner cost $22 and a sales tax of $1.87 was added to the bill. How much would the sales tax be on a $66 dinner? What is the t

ax rate for meals in this city?
Mathematics
1 answer:
alexdok [17]3 years ago
8 0

Answer:

The correct answer is the sales tax charged is $5.61 for $66 dinner at 8.5% tax rate.

Step-by-step explanation:

Cost of the dinner is $22. Tax levied on it is $1.87

Let x% is the rate of tax in the city.

Therefore, x% of 22 = 1.87

⇒ x = 1.87 × \frac{100}{22} = 8.5

Therefore 8.5% is the tax rate in the city on foods.

Now another dinner costs $66.

Tax levied on it at the same percentage is given by 8.5% of 66 = $5.61.

Thus $5.61 as sales tax would be charged for a $66 dinner.

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Given:

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Step 1: Simplify the numerator

$\frac{(4 r)^{3}}{15 t^{4}}=\frac{4^3 r^{3}}{15 t^{4}}=\frac{64 r^{3}}{15 t^{4}}

Step 2: Simplify the denominator

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Step 3: Using step 1 and step 2

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}} \right)}

Step 4: Using fraction rule:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}

$\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}}\right)}=\frac{64r^3 \cdot 9t^2}{16 r \cdot 15 t^4}

Cancel the common factor r and t², we get

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Cancel the common factors 16 and 3 on both numerator and denominator.

           $=\frac{4 r^{2} \cdot 3 }{  5 t^2 }

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The simplified fraction is \frac{12 r^{2}  }{  5 t^2 }.

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