Alexis has 52 coins in her coin purse that are either quarters or nickels. she has a total of $8 in her coin purse.
let q represent the number of quarters and n represent the number of nickels. the following system of equations represents this situation:
n+q=52
0.05n+0.25q=8
how many nickels does alexis have? how many quarters does she have?

To find out, we solve the system of equations.

n + q = 52

n = -q + 52

Plug in -q + 52 for 'n' in the 2nd equation:

0.05(-q + 52) + 0.25q = 8

Distribute 0.05:

-0.05q + 2.6 + 0.25q = 8

Combine like terms:

0.2q + 2.6 = 8

Subtract 2.6 to both sides:

0.2q = 5.4

Divide 0.2 to both sides:

q = 27

Now plug this into any of the two equations to find 'n':

n + q = 52

n + 27 = 52

Subtract 27 to both sides:

n = 25

So Alexis had 27 quarters and 25 nickels.

6x - 42 + x = 15 +9x + 5 ;
7x - 42 = 20 + 9x;
7x - 9x = 20 + 42;
-2x = 62;
x = -31;