Question 60293
This word problem has to do with coins, but I need to solve it by setting up and solving a system of two linear equations in two variables.

Cindy has 43 coins consisting of nickels and dimes.  The total value of the coins is $3.40.  How many coins of each kind does she have?
:
I like to do these in terms of cents to avoid decimals.
Let number of nickles be:n
Let the number of dimes be:d
When we add the coins together we have 43 coins: n+d=43
Nickels are worth 5 cents, so the amount of money in nickels we have is: 5n
Dimes are worth 10 cents: 10d
Total cents when added together: 5n+10d=340
:
E1:  n+d=43
E2:  5n+10d=340
Solve  E1, for one of the variables like d and substitute into E2 and solve for n.
:
E1: n+d=43 --> d=43-n
5n+10(43-n)=340
5n+430-10n=340
-5n+430=340
-5n+430-430=340-430
-5n=-90
-5n/-5=-90/-5
n=18
Substitute that into E1 to see how many dimes there were:
d=43-18
d=25
There were 18 nickels and 25 dimes.
Sanity Check: does 18 nickels and 25 dimes = $3.40?  You decide if we're right.
Happy Calculating!!!