Mathematics, 06.04.2020 02:57 19thomasar

A trip for 681 person group required 12 vans and 9 buses. The next year, 882 people go on the trip and it requires 6 vans and 14 buses. Find the number of people that can fit on a van and on a bus

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Answer from: gaby6951

14 people can fit on a van and 57 on a bus.

Step-by-step explanation:

Given:

A trip for 681 person group required 12 vans and 9 buses. The next year, 882 people go on the trip and it requires 6 vans and 14 buses.

Now, to get the number of people that can fit on a van and on a bus.

Let the number of people fit on a van be

And let the number of people fit on a bus be

So, the total number of people on 12 vans and 9 buses are:

$12x+9y=681\ \ \ \ ...(1)$

And, the total number of people on 6 vans and 14 buses are:

$6x+14y=882\ \ \$

Now, multiplying the above equation by 2 we get:

12x+28y=1764 ....(2)

Then, solving the system of equations by subtracting the equation (1) from equation (2):

$(12x+28y)-(12x+9y)=1764-681\\\\12x-12x+28y-9y=1764-681\\\\19y=1083$

Dividing both sides by 19 we get:

y=57.

The number of people fit on a bus = 57.

Now, to get the number of people fit on a van b y substituting the value of in equation (1):

$12x+9y=681\\\\12x+9(57)=681\\\\12x+513=681$

Subtracting both sides by 513 we get:

12x=168

Dividing both sides by 12 we get:

x=14.

The number of people fit on a van = 14.

Therefore, 14 people can fit on a van and 57 on a bus.

Answer from: Quest

3were boys and 5 were girls

Answer from: Quest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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A trip for 681 person group required 12 vans and 9 buses. The next year, 882 people go on the trip a...

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