A group of students planned to chip in to raise a total of $100 for one of their friends’ birthday party but 5 persons couldn’t come so they didn’t pay. This increased the share of the others by $1 each. Find the amount that each person paid after

$5

Step-by-step explanation:

Let the number of students be x, then

Initial amount per student was:

After it becomes:

Since amount increased after, it can be shown as:

Multiply each term by x(x - 5) to get rid of the fraction:

Positive solution of this quadratic equation is

Amount each person paid after:

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions