A coin bank contains only dimes or nickels,but there are no more than 27 coins.the value of the coins is $2.10.How many different combinations are there of both

Question

It is on a paper and it has to do with math.

Answer 1

Let's call nickels n, and dimes d.

 

We know that the total number of nickels and dimes is equal to 27.

 

n + d = 27

 

Next, we know that the cost-sum is 2.10.

 

A nickel is worth $0.05, and a dime is worth $0.10.

 

0.05n + 0.10d = 2.10

n + d = 27

 

Now this question becomes a system of linear equations.

 

We can use substitution by rewriting the second equation to n = 27 - d

We can replace "n" in the first equation to "27 - d"

 

0.05(27 - d) + 0.10d = 2.10

 

1.35 - 0.05d + 0.10d = 2.10

 

Combine like terms

1.35 + 0.05d = 2.10

 

Subtract 1.35 from each side

0.05d = .75

 

Divide both sides by 0.05

d =15

 

Now that we know what d is, we can insert it back into the second equation:

n + 15 = 27

n = 12

 

There are 12 nickels and 15 dimes in the bank.

 

We can check our answer by inputing these values into the first equation.

 

0.05*12 + 0.10*15 = 2.10

0.6 + 1.5 = 2.10

2.10 = 2.10