GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsHard
A project manager is monitoring the progress of two teams. Team A has completed 15% of the project, and Team B has completed 20%. If 'x' represents the total percentage of the project completed by Team A and 'y' represents the total percentage completed by Team B, and the total completed by both teams must be at least 80% for the project to be on track, which inequality represents this condition?
- A0.15 + 0.20 ≥ 0.80
- Bx + y ≥ 0.80
- Cx + y ≥ 80
- D0.15x + 0.20y ≥ 0.80
Show answer & explanationAnswer & explanation
Correct answer: C. x + y ≥ 80
The variables 'x' and 'y' already represent the total percentage completed by each team. The problem states that the total completed by both teams (x + y) must be 'at least 80%'. The phrase 'at least' translates to 'greater than or equal to' (≥). So, x + y ≥ 80.
Why the other options are wrong
- A. This only sums the given initial percentages, not the total completed by each team represented by x and y.
- B. This represents the percentages as decimals, while the problem implies x and y are whole numbers representing percentages (e.g., 50% is 50, not 0.50).
- D. This incorrectly multiplies the percentages by x and y, implying x and y are not already percentages.
Translating Word Problems to Linear Inequalities
Converting a real-world scenario that involves a range or limit into a mathematical inequality using variables and inequality symbols.
- Identify the unknown quantities and assign variables.
- Look for keywords that indicate inequality symbols (e.g., 'at least', 'no more than', 'less than', 'greater than').
- Formulate the inequality based on the relationships described.
Memory trick: Words to limits, inequality fits!