Final answer:
To find the least number of 16 cent stamps Ben purchased, we can set up a system of equations using the given information. By solving the equations, we find that Ben purchased 29 25 cent stamps and 7 16 cent stamps.
Step-by-step explanation:
To solve this problem, we need to set up a system of equations using the given information. Let's say Ben purchased x 25 cent stamps and y 16 cent stamps. We can then set up the following equations:
0.25x + 0.16y = 3.62 (total cost of stamps)
x + y = (total number of stamps)
By solving these equations simultaneously, we can find the values of x and y. Subtracting the second equation from the first equation, we get:
0.09x = 2.62
x = 29.11 (rounded to the nearest whole number)
Since the number of stamps must be a whole number, Ben must have purchased 29 25 cent stamps. Substituting this value into the second equation, we can find y:
29 + y = (total number of stamps)
29 + y = 36
y = 7
Therefore, the least number of 16 cent stamps Ben purchased is 7.