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trapecia [35]
3 years ago
9

At RSM summer camp 100 students had enough food for a 30-days stay. After 2 days 40 new students joined the camp. After that 2 w

eeks passed and half of the students left the camp. How many additional days of food need to be ordered ?
Mathematics
1 answer:
omeli [17]3 years ago
6 0

Answer:

"no additional days of food need to be ordered."

Step-by-step explanation:

Suppose initial quantity of food is x units

Assuming each student eats 1 unit of food per day,

x = 30 * 100 = 3000 units of food

In 2 days, food eaten:

100 * 1 * 2 = 200 units

So food left after 2 days is  3000 - 200 = 2800 units

Now, there are 140 students. They stay 2 weeks (14 days) - 2 = 12 more days

So food eaten in 12 days:

140 * 1 * 12 = 1680 units

<u>THus, after total 14 days gone, the amount of food left is:</u>

2800 - 1680 = 1120 units

Half students left, so there are 70 students left for the last 16 days. How much food would they need?

70 * 1 * 16 = 1120 units

And there are exactly 1120 units left. So, no additional days of food need to be ordered.

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Piravena must make a trip from A to B then from B to C, then from C to A. Each of these three parts of the trip is made entirely
anyanavicka [17]

Answer:

a) Cost of flying from A to B = $425

b) Total distance travelled by Piravena during the complete trip = 7,500 km

c) To minimize cost and arrive at the final cost given, she must have travelled by bus from B to C and then travelled by taking an airplane from C to A.

Step-by-step explanation:

The complete question is presented in the attached image to this question.

Full Question

a) To begin her trip she flew from A to B. Determine the cost of flying from A to B.

b) Determine the distance she travels for her complete trip.

c) Piravena chose the least expensive way to travel between cities and her total cost was $1012.50. Given that she flew from A to B, determine her method of transportation from B to C and her method of transportation from C to A.

Solution

a) The distance from A to B is given as 3250 km.

To take an airplane, it costs her a $100 booking fee, plus $0.10 per kilometer.

So, to fly 3250 km, she will pay

100 + (0.10×3250) = $425

b) For her complete journey, she is to make a trip from A to B then from B to C, then from C to A.

Her complete distance travelled = AB + BC + CA

But it is given that the three cities form a right angled triangle as given in the question with AB serving as the hypotenuse side.

Pythagoras theorem gives that the square of the hypotenuse side is equal to the sum of the respective squares of the other two sides

AB² = BC² + CA²

3250² = BC² + 3000²

BC² = 3250² - 3000² = 1,562,500

BC = √1,562,500 = 1,250 km

Total distance covered by Piravena during the entire trip = AB + BC + CA = 3250 + 1250 + 3000 = 7,500 km

c) Her total cost of travel = $1012.50

But she definitely flew from A to B at a cost of $425

This means she spent (1012.50 - 425) on the rest of the journey, that is, $587.5

Note that to travel by bus, it is $0.15 per kilometre and to travel by airplane is $100 + $0.10 per kilometre. Indicating that the airplane saves cost on long distance travels while the bus saves cost on short distance travels.

To confirm this, we calculate the two options (bus or airplane) for each route.

If she travels B to C by bus, cost = 0.15 × 1250 = $187.5

If she travels B to C by airplane, cost = 100 + (0.10×1250) = $225

Hence, the bus obviously minimizes cost here.

If she travels from C to A by bus, cost = 0.15 × 3000 = $450

If she travels from C to A by airplane, cost = 100 + (0.10×3000) = $400

Here, travelling by airplane minimizes the cost.

So, if we confirm now that she travelled from B to C by bus and then from C to A by airplane, total cost = 187.5 + 400 = $587.5

which is the remaining part of her total cost is she minimized expenses!

Hope this Helps!!!

7 0
3 years ago
Solve the simultaneous equation<br> X+3y=13<br> X-y=5
Andru [333]

Answer:

x = 7

y = 2

Step-by-step explanation:

In the above question, we are given 2 equations which are simultaneous. To solve this equation, we have to find the values of x and y

x + 3y = 13 ........ Equation 1

x - y = 5...........Equation 2

From Equation 2,

x = 5 + y

Substitute 5 + y for x in Equation 1

x + 3y = 13 ........ Equation 1

5 + y + 3y = 13

5 + 4y = 13

4y = 13 - 5

4y = 8

y = 8/4

y = 2

Since y = 2, substitute , 2 for y in Equation 2

x - y = 5...........Equation 2

x - 2 = 5

x = 5 + 2

x = 7

Therefore, x = 7 and y = 2

5 0
3 years ago
Jack has 5 craft sticks. He needs 4 times that number for a project.how many craft sticks does jack need altogether?
Katarina [22]
Jack would have twenty craft sticks because four times that number is the same as x4 so you would do 5x4=20.
8 0
3 years ago
Read 2 more answers
What is the value of x?<br><br> Enter your answer, as a decimal, in the box.<br><br> cm
kirza4 [7]

Answer:

50.6 cm

Step-by-step explanation:

We can use similar triangles and proportions to solve.  Put the smaller triangle side over the larger triangle side.

x               46.2-14   (This is the length of the short side of the triangle)

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

72.6            46.2

Using cross products

46.2 *x = (46.2-14)  *72.6

46.2 *x = (32.2)  *72.6

46.2 *x = (32.2)  *72.6

46.2x =2337.72

Divide each side by 46.2

46.2/46.2 *x = 2337.72/46.2

x = 50.6

5 0
3 years ago
Solve for the given variable:<br> 14=63n
marin [14]

Answer:

n = 2/9

Step-by-step explanation:

switch sides: 63n=14

divide both sides by 63: 63n/63 = 14/63

simplify: n = 2 / 9

3 0
3 years ago
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