algebra
posted by kayla .
a large group of students want to go to the movies. if the students take 3 vans and 1 car they can transport 22 people. if they take 2 vans and 4 cars. they can transport 28 people.write and solve a system of equations to find the number of people that can be transported in a van. show your work

Question 1
3v + c = 22 (1)
2v + 4c = 28 (2)
From (1)
3v + c = 22
c = 22  3v (3)
Substitute (3) into (2)
2v + 4(22  3v) = 28
2v + 88  12v = 28
10v = 60
v = 6
Therefore, the number of people that can be transported in a van is 6
Respond to this Question
Similar Questions

algebra I
System of Equations I need help with the following problem: A youth group with 26 members is going skiing. Each of the five chaperones will drive a van or a sedan. The vans can seat 7 people and the sedans can seat five people. How … 
Algebra 2
"At a school sponsored car wash, the fees charged were: $5 per car, $8 per truck, $10 per van. Twice as many cars were washed as pickup trucks. The amount collected for washing cars and pickup trucks was $360. A total of $410 was collected. … 
English
1. A group of students help the sick. 2. A group of students helps the sick. (What is the difference between the two sentence? 
Math ratios
The ratio of cars to vans in a parking lot was 5 to 2. There were 28 cars and vans in the parking lot. How many cars were in the parking lot? 
algebra
the senior class at highschool a and highschool b planned separate trips to the local amusement park the senior class at highschool a rented and filled 5 vans and 8 buses with 357 students highschoolb rented and filled 10 vans and … 
Maths
A car showroom had 10y cars, 20y motorcycles and 18 vans. In a particular month, 4y cars , 3y motorcycles and 15 vans were sold. a.) Find the total number of wheels on the remaining vehicles in terms of x. b.) If y=21, how many wheels … 
5TH GRADE MATH
SIXTYSEVEN STUDENTS ARE GOING ON A FIELD TRIP TO THE ZOO. THE PRINCIPAL NEEDS TO DECIDE HOW MANY CARS AND VANS ARE NEEDED TO TRANSPORT THE STUDENTS. EACH CAR CAN SEAT 5 STUDENTS AND EACH VAN SEATS 9. THE PRINCIPAL WOULD LIKE TO USE … 
Math
The parking lot has 5/6 as many vans as trucks. What equation can be use to show the number of vans? 
Math
Am stuck A fifth grade class of 32 students is going on a field trip. They want to rent vans to drive to the field trip. Each van seats a maximum of 7 students. What is the least number of vans the fifth grade class must rent so that … 
Math
n vans each carried 15 people to the soccer game. 30 people arrived in the cars. There were 75 people at the soccer game. How many vans, n, carried people to the soccer game.