Answer:
Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.
Step-by-step explanation:
Let be [tex]x[/tex] and [tex]y[/tex] the amounts of nickels and dimes that Carrie and Joan have, as [tex]c[/tex] the total amount of money that both Carrie and Joan have. A nickel is a five cent coin and a dime is a ten cent coin.
The following equations are constructed after a careful reading on statement:
Carrie's amount of money:
[tex]0.05\cdot x = c[/tex] (Eq. 1)
Joan's amount of money:
[tex]0.10\cdot y = c[/tex] (Eq. 2)
Relation between amounts of coins:
[tex]x = y+40[/tex] (Eq. 3)
First we eliminate [tex]c[/tex] by equalizing (Eq. 1) and (Eq. 2):
[tex]0.05\cdot x = 0.10\cdot y[/tex]
Then, we reduce the resulting formula by (Eq. 3):
[tex]0.05\cdot (y+40) = 0.10\cdot y[/tex]
[tex]y+40 = 2\cdot y[/tex]
[tex]y = 40[/tex]
And rest of variable are now determined:
[tex]x = 40+40[/tex]
[tex]x = 80[/tex]
[tex]c = 0.05\cdot (80)[/tex]
[tex]c = 4[/tex]
Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.
