Adriana has 24 dimes and nickels in a jar. The total value of the coins in the jar is $2.10. How many of each coin does she have?

Question

Adriana has 24 dimes and nickels in a jar. The total value of the coins in the jar is $2.10. How many of each coin does she have?

Answer 1

Hi Maren,

 

d = dimes & n = nickels

 

d + n = 24

 

d = 24 - n

 

(24 - n) 0.10 + (n) 0.05 = 2.10

 

240 -10n + 5n = 210  

(moved 2 decimal places by multiply by 100 to get rid of decimals)

 

-5n = -30   n = 6

 

24 - 6 = # of dimes = 18

 

Let's check it:

 

18 ($0.10) + 6 ($0.05) = 1.80 + 0.30 = $2.10

 

There you have it.  Good luck.

Answer 2

Let x be the number of nickels, and y be the number of dimes. We know that the total number of coins is 24. So our first equation is:

x+y= 24

now, the total value of the coins in the jar is $2:10 (as given). Since each nickel has a value of 5 cents or $0.05, and each dime has a value of 10 cents or $0.10, we can write:

0.05 x + 0.1 y = 2.10

now we have our two equation, and can solve for x and y.

from the first equation:
x = 24-y

put that into the second equation:

0.05 * (24-y) + 0.1y= 2.10

1.2 - 0.05y + 0.1y = 2.10

so 0.05 y = 2.10-1.2 = 0.9 

 

so y = 0.9/0.05 = 18    which means we have 18 dimes (since we chose y as the number of dimes).

 

Now use one of the two equations, and solve for the other variable:

 

x+y= 24 => x= 24-y = 24-18 = 6     which means we have 6 nickles (since we chose x as the number of nickels).

 

And we are done. But let's have a quick check:

 

18 dimes and 6 nickels gives us 24 coins.

 

also 18 dimes = 180 cent = $1.8

6 nickels = 30 cent =$ 0.3

 

total value = 1.8 + 0.3 = $2.10

Answer 3

d+n=24

10d+5n=210

d=24-n

10(24-n)+5n=210

240-10n+5n=210

240-5n=210

-5n=-30

n=6 nickels

d=24-6=18 dimes

6*5+10*18=30+180=210=$2.10