graphing inequality

[Joaquin]

I missed this question on a test and still don't know how to set up the inequality.

Lorenzo's car has an EPA mileage rating of 26 miles per gallon in the city and 32 mpg on the highway. The maximum capacity of the gasoline tank is 14 gallons. Let x represent the number of city miles and y the number of highway miles. Write and graph an inequality for the number of miles Lorenzo can drive without refilling.

Can someone please show me how to set this up?

 

[Deleted member 4993]

I missed this question on a test and still don't know how to set up the inequality.

Lorenzo's car has an EPA mileage rating of 26 miles per gallon in the city and 32 mpg on the highway. The maximum capacity of the gasoline tank is 14 gallons. Let x represent the number of city miles and y the number of highway miles. Write and graph an inequality for the number of miles Lorenzo can drive without refilling.

Can someone please show me how to set this up?

Amount of gas (gallons) used for city driving = x/(26)

Amount of gas (gallons) used for highway driving = ???

Continue....

Please share your work/thoughts with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[Joaquin]

so then -

x/26 less than or equal to 14

y/32 is less than or equal to 14

then y is less than or equal to 448

x is less than or equal to 364

That is two straight lines???

 

[Mrspi]

so then -

x/26 less than or equal to 14

y/32 is less than or equal to 14

then y is less than or equal to 448

x is less than or equal to 364

That is two straight lines???

Well, no...not quite correct.

If x is the number of city miles driven, and the car gets 26 mpg in the city, then x/26 would be the number of gallons of gas used for city driving.

If y is the number of highway miles driven, and the car gets 32 mpg on the highway, then y/32 is the number of gallons of gas used for highway driving.

We are told that the gas tank holds 14 gallons. So, if we are limited to using ONE tank of gas,

gallons used in city + gallons used on highway must be NO MORE than 14 gallons

or,

(x/26) + (y/32) < 14

THAT is the inequality you need to graph.

 

[Deleted member 4993]

There two more (almost trivial) inequalities are involved here:

x ≥ 0 and

y ≥ 0

 

[Mrspi]

There two more (almost trivial) inequalities are involved here:

x ≥ 0 and

y ≥ 0

Thanks, SK....I should have made note of those restrictions!