Mathematics, 18.04.2020 18:01 scoonz1

For a trip, one high school rented and filled 5 vans and 3 buses with 114 students. Another high school instead fit its 247 students into 7 vans and 8 buses. With each bus and van seating the same number of students, how many students could a bus carry? How many students could a van carry?

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Answer from: itziabejar

Therefore a bus could carry 23 number of students and a van could carry 9 number of students.

Step-by-step explanation:

Assume a van and a bus could carry x and y number of students respectively.

Given that,

For a trip, one high school rented and fits 114 students into 5 van and 3 buses.

So,

A van could carry x number of students

5 van could carry 5x number of students.

A buses van could carry y number of students.

3 buses van could carry 3y number of students.

∴5x+3y=114 ....(1)

Another high school instead fit its 247 students into 7 vans and 8 buses.

A van could carry x number of students

7 van could carry 7x number of students.

A buses van could carry y number of students.

8 buses van could carry 8y number of students.

∴7x+8y=247 ....(2)

∴5x+3y=114 ....(1)

and

7x+8y=247 ....(2)

7 times of equation (1) subtracts from 5 times of equation (2)

35x + 40y = 1235

35x + 21y = 798

- - -

________________

40y-21y=1235-798

⇒19y=437

$\Rightarrow y=\frac{437}{19}$

$\Rightarrow y=23$

Putting the value y in equation (1)

5x+3.23=114

⇒5x=114-69

⇒5x=45

$\Rightarrow x=\frac{45}{5}$

⇒ x=9

Therefore a bus could carry 23 number of students and a van could carry 9 number of students.

Answer from: Quest

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be). so point b is at (-2,2). point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

Answer from: Quest

depending on others is critical to survival. my source is apex!

step-by-step explanation:

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