Question

Scott can you help I am confused... Naviah buys at least 8 but no more than 12 gallons of gas each week. The price of gas ranged from 2.25 to 2.50 per gallon each week. Write a compound inequality to model all of the possibilities amount of money (m) Naviah spends on gas each week.

Answer 1

Amount of money Naviah spends each week is ranged from 18 to 30

( 18 ≤ m ≤ 30 )

Explanation:

Let Naviah buys gas each week = x gallons

As given,

Naviah buys at least 8 but no more than 12 gallons of gas each week.

⇒8 ≤ x ≤ 12

Now,

Let the price of gas each week = p

As given,

The price of gas ranged from 2.25 to 2.50 per gallon each week.

⇒2.25 ≤ y ≤ 2.50

Now,

Amount of money spend (m) = (Total gas buy)(Price of gas)

= xy

⇒ m = xy

Now,

we have

8 ≤ x ≤ 12 and 2.25 ≤ y ≤ 2.50

Multiply both the inequality , we get

8×2.25 ≤ x.y ≤ 12×2.50

⇒18 ≤ xy ≤ 30

⇒18 ≤ m ≤ 30

∴ we get

Amount of money Naviah spends each week is ranged from 18 to 30.