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damaskus [11]
2 years ago
11

A group of 24 people need transportation from a hotel to a concert. They will be picked up by Uber drivers that can fit 4 passen

gers in their compact car and 6 passengers in their SUV’s. You would like to determine how many compact cars and SUVs could be used to transport the entire group. Let x = the number of compact cars and let y = the number of SUV's.
Write and graph an equation that models the situation.
Mathematics
2 answers:
devlian [24]2 years ago
5 0

Answer:

4x+6y=24

See below for graph.

Step-by-step explanation:

A total of 24 people need to be transported.

Let <em>x</em> represent the number of Uber compact cars.

And let <em>y</em> represent the number of SUVs.

So, the number of people that can be picked up by <em>x</em> compact cars is 4<em>x</em>.

And the number of people that can be picked up by <em>y</em> SUVs is 6<em>y</em>.

And the total is 24 people. So, the two terms must total 24. So, we can write:

4x+6y=24

We can convert this to slope-intercept form. First, we can divide everything by  2:

2x+3y=12

Subtracting 2<em>x</em> from both sides yields:

3x=-2x+12

Finally, dividing both sides by 3 yields our linear equation:

\displaystyle y=-\frac{2}{3}x+4

Please refer to the below attachment for the graph.

*Note that we should restrain our graph to only QI. This is because we cannot use <em>negative</em> compact cars of SUVs. Also, only <em>integer</em> points on the line will work, as we cannot have, say, 2.5 compact cars.

**Also, the x- and y-intercepts tell us the maximum of each type needed. Either we need 6 compact cars and 0 SUVs, (6, 0); 4 SUVs and 0 compact cars (0, 4); or a combination of them.

andriy [413]2 years ago
3 0

Answer:

Step-by-step explanation:

Compact cars:

24 divided by 4 = 6

6 cars for 24 people

SUV's:

24 divided by 6 = 4

4 SUV's for 24 people

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