Question

A family has a hybrid car that gets 40 miles per gallon (mpg) and a pickup truck that gets 17 mpg. They drive at least 500 miles per week using both vehicles but don't want to use more than 20 gallons of gas. Make a recommendation for using each vehicle. Part A Write an expression that represents the total amount of gasoline used. Then write an inequality to show the maximum amount of gasoline that the family wants to use. Define the variables and list any constraints on the variables.

Answer 1

`Z=x+y`

`x+y<20`

Explanation:

Let the gallons of fuel used in the hybrid per week car be
`x` and
`y` be the number of gallons used in the pickup truck per week.

Number of miles driven using both vehicles is at least 500 per week. The inequality that represents the number of miles driven is.

`40x+17y\geq 500`

The expression of total amount of fuel used would be
`Z=x+y`.

Now the sum of the fuels used in both the cars is more than 20 gallons per week. The inequality that represents the total amount of gasoline used is

`x+y<20`