Name: ______Date: ______Period: ______
Algebra 2: Absolute Value Word Problem Practice
Instructions: Complete each problem, showing all work.
1. TOLERANCE Martin makes exerciseweights. For his 10–pound dumbbells, heguarantees that the actual weight of hisdumbbells is within 0.1 pound of10pounds. Write and solve an equationthat describes the minimum andmaximum weight of his 10-pounddumbbells.
We solve both cases and find the minimum value is 9.9 and the maximum value is 10.1.
Sentence: The min and max weight of the dumbbells are 9.9 and 10.1 pounds, respectively.
2. LOCATIONS Identical vacationcottages, equally spaced along a street,are numbered consecutively beginningwith 10. Maria lives in cottage #17.Joshua lives 4 cottages away fromMaria. If n represents Joshua’s cottagenumber, then |n – 17| = 4. What arethe possible numbers of Joshua’scottage? Use the number line below to explain your answer.
The possible numbers for Joshua’s cottage are between 13 and 21. On the number line, we can find the maximum and minimum using the central value of 17 and the range of 4 (count four in each direction from 17).
3. HEIGHT Sarah and Jessica are sisters.Sarah’s height is s inches and Jessica’sheight is j inches. Their father wantsto know how many inches separatethe two. Write an equation for thisdifference in such a way that theresultwill always be positive no matter whichsister is taller. Explain.
Because we don’t know who is taller, we must use an absolute value. or represent the distance between the two heights on a number line. Both are acceptable answers.
4. AIRPLANESThe ideal weight of one type of model airplane engine is 33.86 ounces. The actual weight may vary from the ideal by at most 0.05 ounce.
a. Write an absolute value inequality to model the situation.
b. Solve your inequality in part a and determine the range of acceptable weights for this engine.
After solving both cases, we find the range of acceptable weight for the engine are between 33.81 and 33.91 ounces.
5. NUMBERS Ian is thinking of an integer. Maria asks Ian “Is the number you’re thinking of within 20 of the number –5?”
a. Ian says yes. Write and solve and absolute value inequality to determine the range of numbers in which Ian number falls. Use a number line to support your explanation.
On the number line, we would shade the numbers that are within 20 spaces from –5 in either direction. It’s an AND inequality, so we shade between –25 and 15, with closed circles at –25 and 15 to include them.
b. Ian says no. Write and solve and absolute value inequality to determine the range of numbers in which Ian number falls. Use a number line to support your explanation.
On the number line, we would shade numbers greatOR than 15 or less than –25. We use open circles to show that those numbers are not included in the solution set.