The Melville Middle School Jazz Band is going on tour of New York City after performing in a competition. The tour company has small vans that can carry 10 passengers other than the driver and large vans that can carry 15 passengers other than the driver.
There are a total of 60 band members and adults from Melville Middle School that are going on the tour. Mr. Goodwin, the band director is trying to figure out the situation.
If x represents the number of small vans and y represents the number of large vans used for the tour of New York City, then which equations represent this situation?
write the equation in standard form and slope-intercept form.
To determine the equations representing this situation, we need to use the following information:
- There are a total of 60 band members and adults going on the tour.
- Each small van can carry 10 passengers other than the driver.
- Each large van can carry 15 passengers other than the driver.
Let's start by writing the equation representing the total number of passengers based on the number of small vans, x, and large vans, y.
Total number of passengers = number of small vans * passengers per small van + number of large vans * passengers per large van
In standard form:
Total number of passengers = 10x + 15y
In slope-intercept form:
Total number of passengers = 10x/15 + y
Mr. Goodwin needs to figure out the minimum number of vans required for the tour, considering that each van should be filled to its maximum capacity. Using this information, we can set up a maximum capacity equation.
Maximum capacity of small vans = number of small vans * 10
Maximum capacity of large vans = number of large vans * 15
In standard form:
Maximum capacity of small vans = 10x
Maximum capacity of large vans = 15y
In slope-intercept form:
Maximum capacity of small vans = 10x/1
Maximum capacity of large vans = 15y/1
Since the number of vans used cannot exceed the total number of passengers, we can set up an equation representing this.
Total number of passengers ≤ Maximum capacity of small vans + Maximum capacity of large vans
In standard form:
60 ≤ 10x + 15y
In slope-intercept form:
60 ≤ 10x/1 + 15y/1
Therefore, the equations representing this situation in both standard form and slope-intercept form are:
Standard form:
Total number of passengers = 10x + 15y
60 ≤ 10x + 15y
Slope-intercept form:
Total number of passengers = 10x/15 + y
60 ≤ 10x/1 + 15y/1
options:
a: 15x + 10y = 60
b: y = -2/3x + 4
c: y=-1.5x+6
d: 2x+3y=12
e: y=-3x+6
f: 3x+2y=12
The correct equations that represent this situation are:
Standard form:
a: 15x + 10y = 60
Slope-intercept form:
c: y = -1.5x + 6
e: y = -3x + 6
just one answer for slope-intercept form please and the correct answer please and thank you
The correct equation in slope-intercept form is:
e: y = -3x + 6