Math / Algebra

Question4 Use the drawing tools to form the correct answer on the provided number line. Daniel is buying gas for his car. Gas costs $\$ 2.50$ per gallon. Daniel typically spends around $\$ 30$ to fill his gas tank, with a variance of up to $\$ 3$ . Write an inequality to model this [situation. Then use the inequality to display the range of possible gallons of gas that Daniel will buy.

Studdy Solution

STEP 1

1. The cost of gas per gallon is $\$2.50$ .
2. Daniel spends around $\$30$ to fill his gas tank.
3. The variance in spending is up to $\$3$ .

STEP 2

1. Set up the inequality based on Daniel's spending range.
2. Solve the inequality to find the range of total cost.
3. Convert the total cost range to the number of gallons of gas.
4. Display the range on a number line.

STEP 3

Set up the inequality based on Daniel's spending range.
Let $x$ be the amount Daniel spends. The inequality for the spending range is: $30 - 3 \leq x \leq 30 + 3$ $27 \leq x \leq 33$

STEP 4

Solve the inequality to find the range of total cost.
The inequality remains the same since it is already solved: $27 \leq x \leq 33$

STEP 5

Convert the total cost range to the number of gallons of gas.
Let $g$ be the number of gallons of gas. Since gas costs $\$2.50$ per gallon, the inequality becomes: $27 \leq 2.50g \leq 33$

STEP 6

Solve for $g$ by dividing each part of the inequality by $\$2.50$ .
$\frac{27}{2.50} \leq g \leq \frac{33}{2.50}$ $10.8 \leq g \leq 13.2$

STEP 7

Display the range on a number line.
The range of possible gallons of gas that Daniel will buy is from $10.8$ gallons to $13.2$ gallons. To represent this on a number line, we would mark the interval $[10.8, 13.2]$ .

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Studdy Solution

STEP 1

1. The cost of gas per gallon is $\$2.50$ .
2. Daniel spends around $\$30$ to fill his gas tank.
3. The variance in spending is up to $\$3$ .

STEP 2

1. Set up the inequality based on Daniel's spending range.
2. Solve the inequality to find the range of total cost.
3. Convert the total cost range to the number of gallons of gas.
4. Display the range on a number line.

STEP 3

Set up the inequality based on Daniel's spending range.
Let $x$ be the amount Daniel spends. The inequality for the spending range is: $30 - 3 \leq x \leq 30 + 3$ $27 \leq x \leq 33$

STEP 4

Solve the inequality to find the range of total cost.
The inequality remains the same since it is already solved: $27 \leq x \leq 33$

STEP 5

Convert the total cost range to the number of gallons of gas.
Let $g$ be the number of gallons of gas. Since gas costs $\$2.50$ per gallon, the inequality becomes: $27 \leq 2.50g \leq 33$

STEP 6

Solve for $g$ by dividing each part of the inequality by $\$2.50$ .
$\frac{27}{2.50} \leq g \leq \frac{33}{2.50}$ $10.8 \leq g \leq 13.2$

STEP 7

Display the range on a number line.
The range of possible gallons of gas that Daniel will buy is from $10.8$ gallons to $13.2$ gallons. To represent this on a number line, we would mark the interval $[10.8, 13.2]$ .

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Studdy Solution

STEP 1

1. The cost of gas per gallon is $2.50\$2.50$2.50.2. Daniel spends around $30\$30$30 to fill his gas tank.3. The variance in spending is up to $3\$3$3.

STEP 2

1. Set up the inequality based on Daniel's spending range.2. Solve the inequality to find the range of total cost.3. Convert the total cost range to the number of gallons of gas.4. Display the range on a number line.

STEP 3

Set up the inequality based on Daniel's spending range.Let xxx be the amount Daniel spends. The inequality for the spending range is: 30−3≤x≤30+3 30 - 3 \leq x \leq 30 + 3 30−3≤x≤30+3 27≤x≤33 27 \leq x \leq 33 27≤x≤33

STEP 4

Solve the inequality to find the range of total cost.The inequality remains the same since it is already solved: 27≤x≤33 27 \leq x \leq 33 27≤x≤33

STEP 5

Convert the total cost range to the number of gallons of gas.Let ggg be the number of gallons of gas. Since gas costs $2.50\$2.50$2.50 per gallon, the inequality becomes: 27≤2.50g≤33 27 \leq 2.50g \leq 33 27≤2.50g≤33

STEP 6

Solve for ggg by dividing each part of the inequality by $2.50\$2.50$2.50.272.50≤g≤332.50 \frac{27}{2.50} \leq g \leq \frac{33}{2.50} 2.5027​≤g≤2.5033​ 10.8≤g≤13.2 10.8 \leq g \leq 13.2 10.8≤g≤13.2

STEP 7

Display the range on a number line.The range of possible gallons of gas that Daniel will buy is from 10.810.810.8 gallons to 13.213.213.2 gallons. To represent this on a number line, we would mark the interval [10.8,13.2][10.8, 13.2][10.8,13.2].

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1. The cost of gas per gallon is $\$2.50$ .
2. Daniel spends around $\$30$ to fill his gas tank.
3. The variance in spending is up to $\$3$ .

1. Set up the inequality based on Daniel's spending range.
2. Solve the inequality to find the range of total cost.
3. Convert the total cost range to the number of gallons of gas.
4. Display the range on a number line.

Set up the inequality based on Daniel's spending range.
Let $x$ be the amount Daniel spends. The inequality for the spending range is: $30 - 3 \leq x \leq 30 + 3$ $27 \leq x \leq 33$

Solve the inequality to find the range of total cost.
The inequality remains the same since it is already solved: $27 \leq x \leq 33$

Convert the total cost range to the number of gallons of gas.
Let $g$ be the number of gallons of gas. Since gas costs $\$2.50$ per gallon, the inequality becomes: $27 \leq 2.50g \leq 33$

Solve for $g$ by dividing each part of the inequality by $\$2.50$ .
$\frac{27}{2.50} \leq g \leq \frac{33}{2.50}$ $10.8 \leq g \leq 13.2$

Display the range on a number line.
The range of possible gallons of gas that Daniel will buy is from $10.8$ gallons to $13.2$ gallons. To represent this on a number line, we would mark the interval $[10.8, 13.2]$ .