To solve this problem, let's assume that there are "x" pencils and "y" jars.
According to the given information, if we put 4 pencils into each jar, we will have one jar left over. This can be represented by the equation:
x = 4y + 1 ----(1)
Similarly, if we put 3 pencils into each jar, we will have one pencil left over. This can be represented by the equation:
x = 3y + 1 ----(2)
To find the values of x and y, we can solve these two equations simultaneously.
By comparing equations (1) and (2), we can see that the value of x is the same in both equations. Therefore, we can equate the right sides of both equations:
4y + 1 = 3y + 1
Simplifying this equation, we get:
y = 0
Substituting this value of y back into equation (1), we can solve for x:
x = 4(0) + 1
x = 1
Therefore, the number of pencils is 1, and the number of jars is 0.
However, the options provided do not match this solution. Let's check the options and select the correct one:
A. 16 pencils, 5 jars
Let's substitute these values into the equations:
For option A, if we put 4 pencils into each of the 5 jars, we should have 20 pencils. However, the given option states that there are only 16 pencils, which does not match the information given.
B. 31 pencils, 10 jars
For option B, if we put 4 pencils into each of the 10 jars, we should have 40 pencils. This does not match the given option of 31 pencils.
C. 32 pencils, 10 jars
For option C, if we put 4 pencils into each of the 10 jars, we should have 40 pencils. This does not match the given option of 32 pencils.
D. 33 pencils, 11 jars
For option D, if we put 4 pencils into each of the 11 jars, we should have 44 pencils. This does not match the given option of 33 pencils.
None of the given options match the solution of 1 pencil and 0 jars. Therefore, there may be an error in the provided options, or the correct answer may not be among the given options.