24 students and teachers rode to the zoo in vans and 385 students and teachers rode to the zoo in buses.
Step-by-step explanation:
Given,
Total number of students and teachers = 409
Students and teachers in each bus = 55
Students and teachers in each van = 12
Let,
x be the number of buses
y be the number of vans
55x+12y=409 Eqn 1
x = y+5 Eqn 2
Putting value of x from Eqn 2 in Eqn 1

Dividing both sides by 67

Putting y=2 in Eqn 2

Number of students and teachers who rode in vans = Number of vans * Teachers and student in each van
Number of students and teachers who rode in vans = 12*2 = 24
Number of students and teachers who rode in buses = 7*55 = 385
24 students and teachers rode to the zoo in vans and 385 students and teachers rode to the zoo in buses.
Keywords: linear equation, substitution method
Learn more about substitution method at:
#LearnwithBrainly
One number is x
other number is 3x-10
x + 3x - 10 = 50
4x = 50 + 10
4x = 60
x = 60/4
x = 15 ← one number
the other number = 3x - 10 = 3*15 - 10 = 35
You add or subtract it for instance: 14x+258-52. You have to subtract 52 from 258 because of the symbol (-) in front of it. Since there is no other numbers with variables 14x is left alone. Hope this helps
Here you have two terms connected by the "subtraction" symbol.
The two coefficients are 2 and 32, and one factor common to both of these is 2. Thus, <span>2x^2-32y^2 = 2(x^2-16y^2).
You could stop here. But it'd make more sense to continue, since x^2-16y^2 is easy to factor:
The three factors of </span><span>2x^2-32y^2 are 2, x-4 and x+4</span>