28 coins; nickles and dimes. Total value of coins $1.95; how many coins of each?

Question

Jessie has 28 coins that are nickels and dimes.  If the value of the coins is $1.95, how many coins of each type does she have?

Answer 1

First, identify the variables:

n = amount of nickels

d = amount of dimes

 

Next, setup the equations based on what you know.  The first equation is:

n + d = 28

 

For the second equation, we know that a dime is worth 10¢ and a nickel is 5¢, so it should be:

0.05n + 0.10d = 1.95

 

This a three-step answer:

1. In one formula (you can use any of them; most people use the simplest one), single out the variable on one side
2. Apply the first formula into the second formula, and solve it to get the value of one variable
3. Apply the answer from the second formula into the first formula, and solve it to get the value of the other variable

 

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Step One:

n + d = 28

n + d - d = 28 - d

n = 28 - d

 

Step Two:

0.05n + 0.10d = 1.95
(0.05 * (28 - d)) + 0.10d = 1.95

1.40 - 0.05d + 0.10d = 1.95

1.40 + 0.05d = 1.95

1.40 - 1.40 + 0.05d = 1.95 - 1.40

0.05d = 0.55

d = 11

 

Step Three:

n = 28 - d

n = 28 - 11

n = 17

 

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Your answer should be 17 nickels and 11 dimes.

 

You can double check by applying the variables into both formulas.

 

n + d = 28

17 + 11 = 28

28 = 28

0.05n + 0.10d = 1.95

(0.05 * 17) + (0.10 * 11) = 1.95

0.85 + 1.10 = 1.95

1.95 = 1.95

 

I hope this helps.

Answer 2

Let n = # nickels

Let d = # dimes

 

From what the problem tells us we can set up 2 equations.

1)  n + d = 28                 There are 28 coins

2)  .05n + .10d = 1.95     Total value of coins is $1.95

 

 

in equation 1 solve for one variable in terms of the other.

from n+d = 28   we can solve for n: 

 

n = 28-d

 

Substitute 28-d in place of n in 2nd equation to solve for # of dimes.

 

.05(28-d) + .10d = 1.95         multiply .05 through the parenthesis

.05(28) - .05d + .10d = 1.95  combine like terms

1.4 + .05d = 1.95                  subtract 1.4 from both sides

.05d = .55                             divide both sides by .05

d = 11

 

There are 11 dimes

 

Since there are 28 total coins and 11 are dimes there are 17 nickels.

 

Check answer:  

.05n + .10d = 1.95

.05(17) + .10(11) = 1.95

.85 + 1.10 = 1.95

1.95 = 1.95