1. ## linear equations in 2 variables....help please

Translate into a pair of linear equations in two variables.
solve the equations using elimination or substitution

Mrs. Boyd has a desk full of quarters and nickels. if she has a total of 25 coins with a total face value of 2.85 , how many are nickels?

I have not been able to figure out how to do this problem and have tried.

2. Originally Posted by southrngrl1966
Translate into a pair of linear equations in two variables.
solve the equations using elimination or substitution

Mrs. Boyd has a desk full of quarters and nickels. if she has a total of 25 coins with a total face value of 2.85 , how many are nickels?

I have not been able to figure out how to do this problem and have tried.
1. Let x denote the number of quarters and y the number nickels.

2. Then you know:

$\left|\begin{array}{rcl}x+y&=&25 \\ 0.25 \cdot x + 0.05 \cdot y&=& 2.85\end{array}\right.$

3. Solve for x and y.

3. Let the number quarters be represented by q, and nickels by n.

The total number of coins is q + n, which is equal to 25.

So, you have

q + n = 25

Now, the value of a nickel is 5 and that of a quarter is 25 (I'm not sure for the value of a nickel, correct me if I'm wrong, it's not my currency).

0.25q gives the value of the total quarters, and 0.05n gives the value of the total nickels.

Their value add up to 2.85.

So,

0.25q + 0.05n = 2.85

You now have:

q + n = 25
0.25q + 0.05n = 2.85

Solve them simultaneously

Post what you get!

EDIT: Oops, didn't know you posted before me earboth

4. Thank you for the help. Now I will be ableto finish this. I had the first part but was not sure if it was right.

THanks again. have a great week