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Katie buys a large pizza for $14.99 and bottles of soda for $1.50 each. If the total cost was $23.99, how many bottles of soda (

Nady [450]

The number of soda bottles Katie bought is 6

The given parameters are:

Large Pizza = $14.99
Soda = $1.50 per bottle
Total cost = $23.99

Assume the number of soda bottle is x.

So, we have:

$Total = Pizza + Soda \times x$

This gives

$23.99 = 14.99 + 1.50\times x$

Subtract 14.99 from both sides of the equations

$9 = 1.50\times x$

Divide both sides of the equations by 1.5

$6=x$

Rewrite the equation as

$x = 6$

Hence, the number of bottles is 6

Read more about linear equations at:

brainly.com/question/14323743

7 0

2 years ago

The ratio of the circumference of two circles is 3:2.What is the ratio of their area

Nezavi [6.7K]

The ratio of their area is 9/4

<h2>Explanation:</h2>

We use ratios to compares values. In this exercise, we are comparing the circumference of two circles, which is:

$3:2$

and we want to know what is the ratio of their area. Recall that the circumference of a circle is given by:

$C=2\pi r \\ \\ \\ Where: \\ \\ C:Circumference \\ \\ r:Radius \ of \ the \ circle$

If we define:

$C_{1}: \ Circumference \ of \ circle \ 1 \\ \\ C_{2}: \ Circumference \ of \ circle \ 2 \\ \\ r_{1}: \ Radius \ of \ circle \ 1 \\ \\ r_{2}: \ Radius \ of \ circle \ 2$

Then, the ratio of the circumference of two circles is 3:2 is:

$\frac{C_{1}}{C_{2}}=\frac{2\pi r_{1}}{2\pi r_{2}}=\frac{3}{2} \\ \\ \therefore \frac{r_{1}}{r_{2}}=\frac{3}{2}$

The area of a circle is given by:

$A=\pi r^2 \\ \\ A:Area \\ \\ r:Radius$

So the ratio of their area can be found as:

$\frac{A_{1}}{A_{2}}=\frac{\pi r_{1}^2}{\pi r_{2}^2} \\ \\ \\ A_{1}:Area \ of \ circle \ 1 \\ \\ A_{2}:Area \ of \ circle \ 2$

So:

$\frac{A_{1}}{A_{2}}=\frac{r_{1}^2}{r_{2}^2}=\left( \frac{r_{1}}{r_{2}} \right)^2 \\ \\ \frac{A_{1}}{A_{2}}=\left(\frac{3}{2}\right)^2 \\ \\ \boxed{\frac{A_{1}}{A_{2}}=\frac{9}{4}}$