Question

8th grade word problem, show steps please (will give brainiest) :)

Answer 1

Answer:

There are 24 students and teachers that rode in vans, and there are 385 students and teachers that rode in buses.

Step-by-step explanation:

First we are going to set up a system of equations where:

b= number of buses

v= number of vans

We know from the equation that each bus transported 55 people and that each van transported 12 people and that there was a total of 409 people transported. We also know that the number of buses was 5 more than the number of vans.

Knowing that we can set up our system:

$\left \{ {{55b+12v=409} \atop {b=v+5\\}} \right.$

Since we know what b is equal to, we can now use the substitution method to plug the value of b from the bottom equation into the one on the top and solve for variable v.

55(v +5)+12v =409

From there we can distribute 55 into (v+5)

55v +275+12v =409

We can now combine like terms.

67v +275 = 409

From there we subtract 275 from both sides of the equation to isolate the variable.

67v +275 = 409

      -275    -275

After doing this, we now divide both sides of the equation by 67 to solve for v.

$\frac{67v}{67} =\frac{134}{67}$

We now know that v, the number of vans is 2 and can plug that into our bottom equation from our system of equations ($b=v+5$).

$b=2+5\\b=7$

Knowing that there are 7 buses and 2 vans, we can now plug these numbers into the terms in the top equation of our system. 55b and 12v.

$55(7)=385$

$12(2)= 24$

385 people rode buses. 24 people rode vans

Check your equation

409 people went in total. 385 + 24 = 409.

Answer 2

person above is correct