QuestionDaniel spends around \$30 on gas at \$2.50 per gallon. Write an inequality to find the range of gallons he can buy.

Studdy Solution

STEP 1

Assumptions1. The cost of gas per gallon is $.50. Daniel typically spends around$ 30 to fill his gas tank3. The variance in the amount Daniel spends is up to N dollars4. The inequality will model the range of possible gallons of gas that Daniel will buy

STEP 2

First, we need to find the typical number of gallons Daniel buys when he spends $30. We can do this by dividing the typical amount Daniel spends by the cost of gas per gallon.
$Typical\, gallons = Typical\, amount\, spent / Cost\, of\, gas\, per\, gallon$

STEP 3

Now, plug in the given values for the typical amount spent and the cost of gas per gallon to calculate the typical number of gallons.
$Typical\, gallons = \$30 / \$2.50$

STEP 4

Calculate the typical number of gallons Daniel buys.
$Typical\, gallons = \$30 / \$2.50 =12\, gallons$

STEP 5

Now that we have the typical number of gallons, we can write an inequality to model the range of possible gallons of gas that Daniel will buy. The inequality will be in the form of $|x - a| \leq b$ , where $x$ is the number of gallons, $a$ is the typical number of gallons, and $b$ is the variance in the number of gallons.
$|x -12| \leq N$

STEP 6

This inequality represents the range of possible gallons of gas that Daniel will buy. The solution to this inequality is $12 - N \leq x \leq12 + N$ , which means Daniel will buy between $12 - N$ and $12 + N$ gallons of gas.

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