Question 139·Easy·Linear Inequalities in One or Two Variables
A hiking club requires each member to attend at least 12 hikes per year. If Malik has already participated in 9 hikes this year, what is the minimum number of additional hikes Malik must join this year to meet the requirement?
For "at least" or "at most" requirement problems, first represent the unknown quantity with a variable, then relate the current amount and the required amount with an inequality (e.g., current + additional ≥ requirement). Solve the simple equation or inequality—often just a subtraction—to find the minimum additional amount needed, and always interpret your result back in words to ensure it answers the question about "how many more."
Hints
Focus on the total required vs. already done
How many hikes does the club require in total, and how many has Malik already completed? Think about the difference between these two numbers.
Use a variable for the unknown number of hikes
Let be the number of additional hikes Malik will attend. How can you express Malik’s total number of hikes in terms of ?
Understand "at least"
The phrase "at least 12 hikes" means the total number of hikes is greater than or equal to 12. What inequality can you write, and what is the smallest value of that makes it true?
Desmos Guide
Use Desmos to find the difference
In the expression line, type 12 - 9 and press Enter. The value that Desmos outputs is the number of additional hikes Malik needs to meet the 12-hike requirement.
Step-by-step Explanation
Translate the situation into math
Let be the number of additional hikes Malik must attend. The requirement is at least 12 hikes in total, and Malik already has 9, so we write:
Here, is Malik’s total hikes after joining more.
Solve the inequality for x
Solve the inequality:
Subtract 9 from both sides:
So must be greater than or equal to the difference between 12 and 9.
Interpret the solution in the context
Compute the difference:
So , which means Malik must go on at least 3 more hikes to meet the requirement. The minimum whole number of additional hikes is 3, which corresponds to answer choice D.