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2 years ago

10

Ava and Greg are selling cookies and popcorn to raise money for a school trip. Ava sold 10 boxes of cookies and 8 bags of popcor

n and raised $102. Greg sold 4 boxes of cookies and 12 bags of popcorn and raised $98. How much is a bag of popcorn?

1 answer:

sladkih [1.3K]2 years ago

5 0

Let x represent number of boxes of cookies and y represent popcorn bags.

We have been given that Ava sold 10 boxes of cookies and 8 bags of popcorn and raised $102. We can represent this information in an equation as:

$10x+8y=102...(1)$

We are also told that Greg sold 4 boxes of cookies and 12 bags of popcorn and raised $98. We can represent this information in an equation as:

$4x+12y=98...(2)$

Now we will use substitution method to solve our system of equations.

Form equation (1), we will get:

$x=\frac{102-8y}{10}$

Upon substituting this value in equation (2), we will get:

$4(\frac{102-8y}{10})+12y=98$

$2(\frac{102-8y}{5})+12y=98$

$\frac{204-16y}{5}+\frac{60y}{5}=98$

$\frac{204-16y+60y}{5}=98$

$\frac{204+44y}{5}=98$

$\frac{204+44y}{5}\cdot 5=98\cdot 5$

$204+44y=490$

$204-204+44y=490-204$

$44y=286$

$\frac{44y}{44}=\frac{286}{44}$

$y=6.5$

Therefore, each bag of popcorn costs $6.5.

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Erik's disabled sailboat is floating stationary 3 miles east and 2 miles north of Kingston. A ferry leaves Kingston heading towa

sergij07 [2.7K]

Answer:

Step-by-step explanation:

Let's suppose that Ballard is an origin with coordinates (0;0)

Ballard is 8 miles south and 1 mile west of Edmonds ⇒ Edmonds is 1 mile east and 8 miles north of Ballard.

Thus, coordinates of Edmonds (0+1; 0+8) (1;8)

Edmonds is 6 miles due east of Kingston. So, is 6 miles due of Edmonds

Thus, Kingston coordinates (1-6;8) (-5:8)

Sailboat is 3 miles east and 2 miles north of kingston

So, coordinates of sailboat are (-5+3; 8+2) (-2;10)

a)

Ferry leaves Kingston towards Edmonds at mph and Edmonds is 6 miles due east of Kingston.

Initial ferry coordinates as calculated above are equal to Kingston coordinates (-5;8)

After 20 minutes the ferry turns to south.

This distance travelled (20min) is d=9mph*20/60h=3 miles

So, ferry travelled 3 miles toward east in 20 min

Then, coordinates became (-5+3;8+0) (-2;8)

Thus, we have a line connecting two points (-5;8) and (-2;8)

Line connecting them has an equation:

y-8 = (8-8)/(-2+5) * (x+5)

y-8=0

y=8 - This is the equation for the first 20 minutes of travel

Then, ferry turns due south (-2;8) and has a vertiacl line

The equation of verical line is x=a, so the equation will be x=2

b) The sailboat has a radar scope that will detect any object within 3 miles of the sailboat.

region looks like a circular disc with a center (-2;10)

(x+2)^2+(y-10)^2=3^2

(x+2)^2+(y-10)^2 <9 (interior of the circular disc)

(x+2)^2+(y-10)^2 >9 (exterior)

The equation of the line joining the Kingston and Edmonds is y=8

the point of intersection:

(x+2)^2+(8-10)^2=9

(x+2)^2=5

x is approximately 0.24; -4.24

(0.24;8) (-4.24;8) - intersection points

c) The ferry exits the radar during the trid due south long x=-2

The points of intersection of the circle and the line x=-2:

(-2+2)^2+(y-10)^2=9

0+(y-10)^2=0

y is 7.13

(-2;7)

d) Takes south turn at (-2;8), then ferry travels 0.8 miles up to point (-2;7) where it exists the radar zone

Speed is 9mph

The time taken to cover 1 mile = t=1/9hr=1/9 *60=6.667min

So, it exists after 6.67 minutes

e) Ferry enters at (-4.24;8) and takes turn due to south at (-2;8)

The distance travelled is = [-4.24+2]=2.24 miles

The time taken to cover these miles is = t=2.24/9 *60=14.93 min

After turning to south ferry remains in radar for 6.7 min

So, it remains in radar zone for 14.93+6.7=21.63min

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2 years ago

What type of triangle has side lengths 12, 13, and 2√3?

Travka [436]

Answer:

The triangle is an obtuse scalene triangle

Step-by-step explanation:

we know that

if $c^{2}=a^{2}+b^{2}$ --------> is a right triangle

if $c^{2}>a^{2}+b^{2}$ --------> is an obtuse triangle

if $c^{2}$ --------> is an acute triangle

where

c is the greater side

we have

$c=13\ units$

$a=12\ units$

$b=2\sqrt{3}\ units$

so

$c^{2}=13^{2}=169$

$a^{2}+b^{2}=12^{2}+(2\sqrt{3})^{2}=156$

so

$c^{2}>a^{2}+b^{2}$ -------> is an obtuse triangle

Remember that

The given triangle has three different length side

so

Is a scalene triangle

therefore

The triangle is an obtuse scalene triangle

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2 years ago

I helped 3.6 customer per half hour yesterday. so i helped _____ customers in 7.5 hour yesterday

Serggg [28]

3.6 customers x customers

-------------------- = ----------------

.5 hours 7.5 hours

using cross products

3.6 * 7.5 = x * .5

divide by .5 on each side

3.6 * 7.5 / .5 =x

54 =x

You can help 54 customers

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2 years ago

Can u solve this pls easy? A geologist takes samples of two rocks from a mountainside. The gray rock has a volume 25% higher tha

Korolek [52]

Answer:

Text me back for an answer.

Step-by-step explanation:

Make sure you text back.

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2 years ago

When Gene and Kelly were planning their trip to Paris, one United States dollar was worth about $\frac{7}{10}$ of a euro. Before

Andre45 [30]

Answer:

$280 dollars

Step-by-step explanation:

When they were leaving

$\$1 \approx \frac{7}{10}$ Euro\\Therefore:\\\$1000 \approx \dfrac{7}{10}\times 1000 =700$ Euro$

When they returned home, they brought 196 Euros.

$If\:\:\$1 \approx \frac{7}{10}$ Euro\\Then: 1 Euro $=\$ \dfrac{10}{7}\\\\$Therefore:\\\\196 Euros = \$ 196 \times \dfrac{10}{7} =\$280$

They brought back $280 dollars to the United States.

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2 years ago

Read 2 more answers