1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kap26 [50]
3 years ago
13

Grant Valley School has hired a fleet of buses and vans to transport 96 students to a picnic. Each bus can seat 31 people, and e

ach van can seat 9 people. The school authorities want to have three teachers traveling in each bus and one teacher in each van.
It will take to accommodate 107 people, including the students and teachers, with no seats left vacant.
NextReset
© 2017 Edmentum. All rights reserved.
Mathematics
2 answers:
Eddi Din [679]3 years ago
5 0

Let x be the<u> number of buses</u> and y be the <u>number of vans</u> needed to transport 107 people.

1. If each bus can seat 31 people and 3 of them should be teachers, then x buses can seat (31-3)x=28x students. If each van can seat 9 people and 1 of them should be teacher, then y vans can seat (9-1)y=8y students.

2. Grant Valley School has hired a fleet of buses and vans to transport 96 students to a picnic.Thus,

28x+8y=96.

3. It will take to accommodate 107 people, including the 96 students and teachers, then the number of teachers is 107-96=11.

x buses will take 3x teachers and y vans will take y teachers,

Therefore, 3x+y=11.

4. Solve the system of equations:

\left\{\begin{array}{l}28x+8y=96\\3x+y=11\end{array}\right.\Rightarrow \left\{\begin{array}{l}28x+8(11-3x)=96\\y=11-3x\end{array}\right..

Solve the first equation:

28x+88-24x=96,\\ \\4x=8,\\ \\x=2.

Then y=11-3x=11-6=5.

Answer: 2 buses and 5 vans

77julia77 [94]3 years ago
4 0
2 buses and 5 vans............
You might be interested in
Which equation is correct? 2x+38) - 5x +4 A 7x - 41 B 7x + 41 C 36x - 2<br>or just write your own
bija089 [108]

Answer:

-3x+42

Step-by-step explanation:

(2x+38) - 5x +4

2x+38 - 5x +4

2x+38+ - 5x +4

2x+-5x+38+4

-3x+42

5 0
3 years ago
Hey I really need this done asap I will mark brainliest and rate 5 stars 50 Points to who ever can get me the answers please and
zavuch27 [327]
                      MUSTARD MAN
1) 16y+0=0  Identity Property Of Addition
2) d*r=r*d     Commutive property of multiplication 
3) 27a*0=0   Identity Property of Addition
4) 16x+5y=5y+16x  Commutive property of Addition
5) r*1=r   Identity property of Addition
6) (5y+2)+14x=5y+(2+14x)   Associate property of Addition 
7) (m*n)*p=m*(n*p)  Associate Property of Multiplication
Please use the information you have to make sure these are RIGHT!!!! 
-GENERAL OUT
4 0
3 years ago
Please help. I have attached a picture.
Ksivusya [100]
Answer: Choice C) -1/3

The given line has a slope of -1/3 so anything parallel to that given line is also going to have an equal slope (of -1/3)

To find the slope of that line shown, notice how we drop down 1 unit and the move to the right 3 units when we go from the left point to the right point. Alternatively, you can use the slope formula m = (y2-y1)/(x2-x1) to get the same result.

7 0
3 years ago
Help answer if u know
Setler [38]

Answer:

b = 6 / 1/4

Step-by-step explanation:

C)

7 0
3 years ago
Read 2 more answers
Which angle has a sine of -1/2 and a cosine of -√3/2
Sergeeva-Olga [200]
\sin x=-\dfrac{1}{2} < 0\\\\\cos x=-\dfrac{\sqrt3}{2} < 0\\\\therefore\ x\in(180^o;\ 270^o)

\text{We know:}\ \tan x=\dfrac{\sin x}{\cos x}\\\\\text{therefore:}\ \tan x=\dfrac{-\frac{1}{2}}{-\frac{\sqrt3}{2}}=\dfrac{1}{2}\cdot\dfrac{2}{\sqrt3}=\dfrac{1}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}=\dfrac{\sqrt3}{3}

\tan x=\dfrac{\sqrt3}{3}\Rightarrow x=30^o+180^o\cdot k;\ k\in\mathbb{Z}

x\in(180^o;\ 270^o)\ therefore\ \boxed{x=30^o+180^o=210^o}
8 0
3 years ago
Other questions:
  • If AB = 21 centimeters, and BC = 28 centimeters, which does AC equal?
    11·1 answer
  • Can someone help me please .. I NEED HELP ASAP .
    14·2 answers
  • Please help!
    13·2 answers
  • A formal power series over R is a formal infinite sum f = X[infinity] n=0 anxn, where the coefficients an ∈ R. We add power seri
    12·1 answer
  • I have 1000 mangos+15000 staberries+200 oranges how many is for this put your enter please thankyou
    13·2 answers
  • You received a bill for $82.53. You prepaid on a budget plan for $110.00/ mth. How much was
    13·1 answer
  • How do I do 6765 divided by 55 in long division
    10·2 answers
  • In the trapezoid, what is the measure of 1?
    10·1 answer
  • A little help please! make sure you read it all
    15·2 answers
  • The winter clothing drive has received donations of 5 coats,23 pairs of gloves, 19 scarves, and 3 hats so far.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!