Question 88·Easy·Linear Equations in One Variable
A teacher purchased 68 pens to give 5 pens to each student in her class. After handing out the pens, she had 8 pens remaining.
How many students are in her class?
For word problems about equal groups, first translate the story into a simple arithmetic relationship or equation. Identify the total amount, subtract anything left over or unused, and then divide by the amount per person to get the number of people (or objects) in each group. Always check your answer by plugging it back into the situation to see if the total and the leftovers match the original description.
Hints
Focus on the pens that were handed out
You know the teacher bought 68 pens and had 8 left after handing them out. How can you find how many pens were actually given to students?
Use subtraction first
Compute to find the total number of pens that were distributed to students.
Connect pens to students
Once you know how many pens were given out, remember that each student gets 5 pens. What operation will tell you how many groups of 5 fit into the total pens given?
Desmos Guide
Compute using an expression
In Desmos, type (68 - 8) / 5 and press Enter. The displayed value of the expression is the number of students.
Alternative: Use an equation and intersection
You can also graph the two equations y = 5x + 8 and y = 68. Then, find the point where the two graphs intersect; the -coordinate of this intersection represents the number of students.
Step-by-step Explanation
Understand what the numbers represent
The teacher bought 68 pens total. After giving 5 pens to each student, she still has 8 pens left. That means some of the 68 pens were handed out and 8 were not handed out.
Find how many pens were actually given to students
Subtract the remaining pens from the total to find how many were handed out:
So, 60 pens were given to the students.
Relate pens given to number of students
Each student gets 5 pens, and together they received 60 pens. To find the number of students, divide the total pens given by the pens per student:
So there are 12 students in the class, which corresponds to choice B.