Help with math hw?Answer the 2nd one

Convert the statements into equations. We can use 'q' for quarters and 'n' for nickels.

"Jenny has $5.05 in quarters and nickels"
[tex]\sf 0.25q+0.05n=5.05[/tex]

"Jenny only has 25 coins"
[tex]\sf q+n=25[/tex]

Solve for one of the variables in the 2nd equation, then plug that into the first equation:

[tex]\sf q+n=25[/tex]

Subtract 'n' to both sides:

[tex]\sf q=25-n[/tex]

Now input '25-n' for 'q' in the first equation:

[tex]\sf 0.25q+0.05n=5.05[/tex]

[tex]\sf 0.25(25-n)+0.05n=5.05[/tex]

Distribute 0.25 into the parenthesis(we do this by multiplying it to every term inside of it):

[tex]\sf 6.25-0.25n+0.05n=5.05[/tex]

Combine like terms(-0.25n + 0.05n = -0.20n):

[tex]\sf 6.25-0.20n=5.05[/tex]

Subtract 6.25 to both sides:

[tex]\sf -0.20n=-1.20[/tex]

Divide -0.20 to both sides:

[tex]\sf n=6[/tex]

So she has 6 nickels, now we can plug this into any of the two equations to find 'q':

[tex]\sf q+n=25[/tex]

[tex]\sf q+6=25[/tex]

Subtract 6 to both sides:

[tex]\sf q=19[/tex]

So she has 19 quarters and 6 nickels.