Your piggy bank has a total of 41coins in it; some are dimes and some are nickels. If you have a total of $3.4?

Let the number of dimes = x

Let the number of nickles = y

x + y = 41 <--- This shows the total number of coins.

0.1x + 0.05y = $3.45 <---- This shows the dollar value of all the coins.

You want to get one variable alone on one side of an equation.

x + y = 41

subtract y from both sides of the equation

x = 41 - y

Now you use substitution. In the second equation replace the x with (41 - y).

0.1(41 - y) + 0.05y = $3.45 (this gives you one variable to deal with)

multiply the clear the parentheses

4.1 - 0.1y + 0.05y = 3.45

combine like terms

4.1 - 0.05y = 3.45

add 0.05y to both sides of the equation

4.1 = 3.45 + 0.05y

subtract 3.45 from both sides of the equation

0.65 = 0.05y

divide by 0.05y on both sides of the equation

13 = y <==== ANSWER (the number of nickles)

Now substitute 13 for the y in the first equation.

x + 13 = 41

subtract 13 from both sides of the equation

x = 28 <==== ANSWER (the number of dimes)

You can check your answer by substituting both numbers into either or both of the original equations.

Have a great day!

D = number of dimes (with a value of 10D cents)

N = number of nickles (with a value of 5N cents)

so N + D = 41 (total number of coins)

and 5N + 10D = 345 (total value, in cents)

multiply the first equation by 5: 5N + 5D = 205

subtract this new equation from the second equation to get

0 + 5D = 140, or D = 28

so N = 41-28 = 13

28 dimes and 13 nickles.

---------------

check : 28 + 13 = 41 coins in all

value = $2.80 + $0.65 = $3.45.