Ask question

Ask question

All categories

2 years ago

5

Sarah and her children went into a movie theater and she bought $35.50 worth of drinks and candies. Each drink costs $5 and each

candy costs $4.25. She bought 3 times as many candies as drinks. Determine the number of drinks and the number of candies that Sarah bought.

1 answer:

Scilla [17]2 years ago

4 0

Answer:

The number of drinks that Sarah bought was 2 and the number of candies that Sarah bought was 6

Step-by-step explanation:

Let

x ----> the number of drinks that Sarah bought.

y ----> the number of candies that Sarah bought.

we know that

she bought $35.50 worth of drinks and candies

so

$5x+4.25y=35.50$ -----> equation A

She bought 3 times as many candies as drinks.

so

$y=3x$ -----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (2,6)

see the attached figure

therefore

The number of drinks that Sarah bought was 2 and the number of candies that Sarah bought was 6

You might be interested in

Find all points on the circle (x^2) + (y^2) = 676 where the slope is 5/12

borishaifa [10]

Implicit defferentation

remember that dy/dx y= dy/dx

so
take derivitive of both sides
$2x+2y \space\ \frac{dy}{dx}=0$
solve for $\frac{dy}{dx}$
minus 2x both sides
$2y \space\ \frac{dy}{dx}=-2x$
divide both sides by 2y
$\frac{dy}{dx}=\frac{-2x}{2y}$
$\frac{dy}{dx}=\frac{-x}{y}$

when is the slope equal to $\frac{5}{12}$
solve for $\frac{dy}{dx}=\frac{5}{12}$
$\frac{dy}{dx}=\frac{5}{12}$
$\frac{5}{12}=\frac{-x}{y}$
$5y=-12x$
$y=\frac{-12}{5}x$
find where the circle and this line intersects

substitute $\frac{-12}{5}x$ for y
$x^2+(\frac{-12}{5}x)^2=676$
$x^2+\frac{144}{25}x^2=676$
$\frac{25}{25}x^2+\frac{144}{25}x^2=676$
$\frac{169}{25}x^2=676$
times both sides by $\frac{25}{169}$
$x^2=100$
sqrt both sides, take positive and negative roots
x=+/-10

sub back

$y=\frac{-12}{5}x$
$y=(\frac{-12}{5})(10) \space\ or \space\ (\frac{-12}{5})(-10)$
$y=\frac{-120}{5} \space\ or \space\ \frac{120}{5}$
$y=-24 \space\ or \space\ 24$

the points are (10,-24) and (-10,24)

8 0

2 years ago

Identify the GCF of 6x2y2 − 8xy2 + 10xy3. 6x2y2 2x2y 2xy2 6xy2

sattari [20]

First find GCF of the numbers:-

GCF of 2, 6 and 8 = 2
GCF od x^2 x and x is x
GCF of y^2, y^2 and y^3 is y^2

so the answer is 2xy^2

The third choice.

3 0

2 years ago

Read 2 more answers

Help me pleaseeee!!!!!

Julli [10]

Because she needs 3 blankets and it takes 15 day per blanket(rate is given), she needs 3x15 or 45 days. She has 60 days so she can volunteer at most 15 days.

answer: s≤15

4 0

2 years ago

Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decel

DedPeter [7]

Answer:

37.5 revolutions

Step-by-step explanation:

The average rotation speed for the first second and for the last two seconds is:

$V_1 = \frac{0+500}{2}\\ V_1 = 250\ rpm$

For the next 3.0 seconds, the rotation speed is V = 500 rpm.

The total number of revolutions, converting rpm to rps, is given by:

$n=\frac{1*V_1+3*V+2*V_1}{60}\\n=\frac{1*250+3*500*2*250}{60}\\n=37.5\ revolutions$

The DVD makes 37.5 revolutions.

6 0

2 years ago

A computer sells for $ 900 $900dollar sign, 900 and loses 30 % 30%30, percent of its value per year. Write a function that gives

Kazeer [188]

Answer:

The value of the computer is given by $900(0.7)^{t}$ .

Step-by-step explanation:

A computer sells for $900.

If the price of the computer loses 30% of its value per year, then it is compounded every year.

Now, the price of the computer t years after it is sold will be

$900(1 - \frac{30}{100})^{t} = 900(0.7)^{t}$ ........... (1)

Therefore, the value of the computer is given by the above equation (1). (Answer)

8 0

2 years ago

Read 2 more answers