Daniel has $2.05 in nickels and quarters.If he has a total of 13 coins, how much nickels does he have ?

Question

has to do with nickels and quarters 

Answer 1

Let nickels be n and quarters be q.  total number of coins is 13.

 

n + q = 13.----------------------------------- Equation (1) 

 

Now include the value of the coins.

 

0.05 n + 0.25 q = 2.05 --------------------- Equation (2)

 

There are two variables in two equations.  You can solve this by elimination or substitution.

Let's try substitution.  In equation (1), express n in terms of q by subtracting q from both sides.

 

n + q = 13

 

n  = 13 - q

 

Now, substitute n = 13 - q in to equation (2)  and solve for q.

 

0.05 n + 0.25 q = 2.05

 

0.05 ( 13 - q ) + 0.25 q = 2.05

 

Distribute and combine like terms:

 

0.65 - 0.05 q + 0.25 q = 2.05

 

0.65 +  0.2 q = 2.05

 

0.65 - 0.65 + 0.2 q = 2.05 - 0.65 ----------- subtract 0.65 from both sides

 

0.2 q = 1.4 

 

0.2 q / 0.2 = 1.4 / 0.2 ------------------------divide both sides by 0.2

 

q = 7

 

Substitute q = 7 into equation (1) and solve for n.

 

n + q = 13

 

n + 7 = 13

 

n + 7 -7 = 13 - 7 ---------------------- subtract 7 from both sides

 

n = 6.

 

There are 6 nickles and 7 quarters.

 

Check the answer by substituting in to equation (2) to see the equation will be balanced.

 

0.05 n + 0.25 q = 2.05

 

0.05 (6) + 0.25 (7) = 2.05

 

0.30 + 1.75 = 2.05

 

2.05 = 2.05.