Math problem - Number of Coins

Shirley has 47 coins in a jar. The jar contains only dimes and nickels and the value of the coins is $3.20.
>Write and solve a linear system to find the number of dimes and number of nickels in Shirley's Jar

Please help! I dont know how to set this up!

First, we need to define the variables. Let d be the number of dimes and n be the number of nickels.

Next, we need to set up a linear system, or two equations with two variables.
d+n=47 -- total number of coins she has
0.1d+0.05n=3.20 -- total amount of money she has in her jar

Let's multiply the second equation by 20 to eliminate the decimals and to make our lives easier, so the second equation will become:
2d+n=64

Now, let's use elimination to eliminate one of the variables.
2d+n=64
- (d+n=47)
-------------------
d=17

Now, we know that she has 17 dimes. We just need to find how many nickels she has.

d+n=47 -- first original equation
17+n=47 -- substitute 17 for d
n=30 -- subtract 17 on both sides.


Therefore, she has 30 nickels and 17 dimes.


Check:
d+n=47
17+30=47
47=47 -- Correct!

0.1d+0.05n=3.2 -- second original equation; always check with the original equations instead of the equations we simplified into.
0.1(17)+0.05(30)=3.2
1.7+1.5=3.2
3.2=3.2 -- Correct!

Since both of my equations are true, my answer is correct.

Hope this helps!

I salute you, The Troll! Commendable honors upon ye!

Okay, onto the problem.

First, divide each side by wheel ◘
(47*10/5)/◘=3.2/◘
921.54389=0.98427
Now, square each side by ß
921.54389/ß=0.98427/ß
2.7864=5.4
Thereäs zour answer- trolololo deutsch ÖD

Dimes
17

Nickels
30