Question

Some number of pencils are allocated to three students, A,B and C. At the start it is known that student B has the greatest number of pencils while student A has the least number of pencils and Student C with is less that Student B but more than Student A. Because of this it was redristributed in the following manner. On the first allocation. Student B gives up 3/4 of his current pencils where in 1/5 of this when to Student A while 4/5 of it went to Student B. On the second allocation Student C gives up 48 pieces of his pencils where in Student A and B share equally. After the redistribution esch student A, B and C has 44 pencils did student A have initially? ​

Answer 1

Using the information provided and solving a system of equations, it is determined that student A initially had 8 pencils.

Step-by-step explanation:

The question is asking for a mathematical solution to determine the initial number of pencils that student A had. We are given that after redistribution, each student A, B, and C has 44 pencils. We start by setting up the initial number of pencils for B and C with A having the least, B the most, and C in between. Let the initial number of pencils A had be x, B had y, and C had z. We need to solve for x using the information given.

For the first allocation, B gives up 3/4 of his pencils, so that leaves B with y - 3/4y. A receives 1/5 of this amount, so A receives (3/4y)*(1/5) = 3/20y. C gives up 48 pencils in the second allocation, leaving C with z - 48. A and B share this equally, so A receives an additional 24 pencils.

After these transactions, A has x + 3/20y + 24 = 44, B has y - 3/4y + 24 = 44, and C has z - 48 = 44.

We now have a system of equations which are:

1. x + 3/20y + 24 = 44
2. y/4 + 24 = 44 (After simplifying B's pencils)
3. z - 48 = 44

Solving for y and z in equations (2) and (3), we get y = 80 and z = 92. Substituting y into equation (1), we get x as the subject,

x + 3/20*80 + 24 = 44

x + 12 + 24 = 44

x + 36 = 44

So, x = 44 - 36 = 8. Therefore, student A initially had 8 pencils.