Question

Hugo is pumping regular gas into his truck.Write and wolve an absolute value equation to represent how many galloons of gas will he pumped when the total is $25 plus or minus $0.50

Answer 1

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Answer:

              $9.8gallons\leq x\leq 10.2gallons\\ \\ \ [9.8gallons,10.2gallons]$

Both are different forms to represent the same: the amount of gas is between 9.8 gallons and 10.2 gallons, including the borders.

Explanation:

1. Relation between the number of gallons of gas pumped and the total amount paid:

$Number\text{ }of\text{ }gallons=amount\text{ }paid(\ )/price(\ /gallon)$

2. Conversion

The amount paid is said to be $ 25 ± $0.50

To transform that into number of gallons, divide by the price of the regular gas: $2.50/gallon

$Number\text{ }of\text{ }gallons=\ 25/(\ 2.50/gallon)\pm 0.50/(\ 2.50/gallon)$

$Number\text{ }of\text{ }gallons=10gallons\pm0.2gallon$

3. Absolute value equation (inequality)

• 10 gallons ± 0.2 gallons converted to an absolute value inequality is:

              $|x-10gallons|=0.2gallons$

Solution:

$-0.2\leq x-10\leq 0.2$

$-0.2+10\leq x\leq 0.2+10$

$9.8\leq x\leq 10.2$

Hence, the solution is:

           $9.8gallons\leq x\leq 10.2gallons\\ \\ \ [9.8gallons,10.2gallons]$