41 coins, consisting of nickels and quarters, have a total value of $4.65. how many coins of each kind are there?

28 nickels and 13 quarters

Step-by-step explanation:

Let the number of nickels represented by x and the number of quarters represented by y.

Then according to the question, we have the following equations :

Divide 0.05 on both sides  of equation (2), we get

Subtract equation (1) from equation (3) , we get

From (1), x=28

Therefore, there are 28 nickels and 13 quarters.

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