Problema Solution
Pam has a collection of nickels and dimes that is worth $2.15. If the number of dimes was doubled and the number of nickels was increased by 28, the value of the coins would be $4.65. How many nickels and dimes does he have?
Answer provided by our tutors
Let x denote the number of nickels and y denote the number of dimes.
Since a nickel is 5 cents and a dime is 10 cents, we see that x nickels are worth 5x cents and y dimes are worth 10y cents. Then, because the coins are worth $2.15, we have:
5x + 10y = 215 ==> x + 2y = 43.
Then if we double the number of dimes (giving 2y dimes) and increase the number of nickels by 28 (giving x + 28 nickels) to get $4.65, we have:
5(x + 28) + 10(2y) = 465
==> x + 28 + 4y = 93, by dividing both sides by 5
==> x + 4y = 65.
Subtracting the first equation from the second yields:
(x + 4y) - (x + 2y) = 65 - 43
==> 2y = 22
==> y = 11.
Then, since x + 2y = 43:
x + 22 = 43 ==> x = 21.
Therefore, Pam has 21 nickels and 11 dimes.