|
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.
|
|
|
| |
