SOLUTION: Solve and graph the inequality. You have two cars. The first car travels an average of 16 miles on a gallon of gasoline, and the second averages 22 miles per gallon. Suppose you

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Question 1052481: Solve and graph the inequality. You have two cars. The first car travels an average of 16 miles on a gallon of gasoline, and the second averages 22 miles per gallon. Suppose you can afford to buy up to 20 gallons of gas this month. If the first car is driven x miles, and the second car, y, shade the region that gives all possible values of x and y that will keep you from buying more than 20 gallons of gas this month. How do i figure out the value of x and the value of y? I'm confused because it seems like it should be 16x+22y is less than or equal to 20 but i don't know how to solve it or if I'm not suppose to make and equation? but i know for sure that i need a boundary for x and y. i mean its 16 miles for one gallon and 22 gallons for another gallon on 2 different cars and only 20 gallons so wouldn't that be 16x20 and 22x20 but i think the sum has to be 20 so both can't equal 20 and my graph dent have partial numbers only 0,50,100,150,200 and so on.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
The problem description is not complete, so this is the biggest difficulty.

Two different cars, each with its own fuel efficiency ( a uniform rate for each car), and different quantity of gallons used for each car to make a total fuel quantity in gallons. Nothing described about distance!

Tabulating the description shows you:
               FUEL EFFICIENCY (miles/gal)    VOLUME (gal)   DISTANCE (miles)
CAR ONE                16                        x             (  )
CAR TWO                22                        y             (  )
Total/s                                         20             (  )

R*V=D shows a basic rule to relate fuel efficiency, fuel volume, and distance.

The only meaningful equation you can make here is .

Upon further thinking, the fuel efficiency data are not important. This is not really a uniform rates problem. What you are really looking for is x+y<=20, and both x and y must be restricted to between 0 and 20. Negative numbers for x or y not allowed.
Answer by ikleyn(52852)   (Show Source): You can put this solution on YOUR website!
.
Solve and graph the inequality. You have two cars. The first car travels an average of 16 miles on a gallon of gasoline,
and the second averages 22 miles per gallon. Suppose you can afford to buy up to 20 gallons of gas this month.
If the first car is driven x miles, and the second car, y, shade the region that gives all possible values of x and y
that will keep you from buying more than 20 gallons of gas this month.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

They ask you ". . . shade the region that gives all possible values of  x and  y . . .".


So, in a coordinate plane your region is the triangle below the straight line 
16x + 22y = 20

and constrained by (positive) axes of coordinates x and y.

Shade it.

The set of your solutions is the set of points inside this triangle.

What's all.

As usual, when the tutor "josgarithmetic" writes about word problems,
he doesn't understand that his writing is not relevant and not adequate to the problem.

Simply ignore it.


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