7) The senior classes at High School A and High School B planned separate trips to
Yellowstone National Park. The senior class at High School A rented and filled 2 vans
and 7 buses with 407 students. High School B rented and filled 1 van and 7 buses with
389 students. Every van had the same number of students in it as did the buses. How
many students can a van carry? How many students can a bus carry?

Number of students in each van = 18

Number of students in each bus = 53

Step-by-step explanation:

Given: The senior class at High School A rented and filled 2 vans  and 7 buses with 407 students.

High School B rented and filled 1 van and 7 buses with  389 students.

Also, every van and the van had the same number of students in it.

Solution:

Let x denotes number of students in each van and y denotes number of students in each bus.

According to the given information,

From (ii), put in (i)

Put in

Number of students in each van = 18

Number of students in each bus = 53

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.