SOLUTION: Emma Hodges has a jar containing 65 coins, all of which are either nickels or dimes. The total value of the cons is $5.30. How many of each does she have?

Question 1102980: Emma Hodges has a jar containing 65 coins, all of which are either nickels or dimes. The total value of the cons is $5.30. How many of each does she have?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
n = number of nickels.
d = number of dimes.

first equation is n + d = 65

a nickel is worth 5 cents.
a dime is worth 10 cents.
5 dollars and thirty cents is worth 530 cents.

second equation is 5n + 10d = 530

you have 2 equations that need to be solved simultaneously.

they are:

n + d = 65
5n + 10d = 530

from the first equation, solve for n to get n = 65 -d.

in the second equation, replace n with 65 - d to get 5 * (65 - d) + 10d = 530.
simplify to get 325 - 5d + 10d = 530
combine like terms to get 325 + 5d = 530
subtract 325 from both sides of this equation to get 5d = 205
solve for d to get d = 205/5 = 41

since n + d = 65, n must be equal to 24 because 41 + 24 = 65.

you have:

n = 24
d = 41

n + d = 65
5n + 10d = 5*24 + 10*41 = 120 + 410 = 530

solution looks good.

solution is she has 24 nickels and 41 dimes in the jar.

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