Jacob has 3 times as many nickels as half dollars. He has 50 fewer quarters than nickels. Altogether, Jacob has 209 coins. How many quarters does Jacob have?
n+q+h = 209
n = 3h
q = n-50
Now solve for q:
q+50 + q + (q+50)/3 = 209
he has 61 quarters
x + 3x + 3x - 50 = 7x - 50 = 209
7x = 259
x = 37
3 * 37 - 50 = 111 - 50 = 61
To find the number of quarters Jacob has, we need to first set up equations using the information given in the problem.
Let's assume Jacob has x half dollars.
Jacob has 3 times as many nickels as half dollars, so he has 3x nickels.
Jacob also has 50 fewer quarters than nickels, so he has (3x - 50) quarters.
Altogether, Jacob has 209 coins, so the equation becomes:
x + 3x + (3x - 50) = 209
Combine like terms:
7x - 50 = 209
Add 50 to both sides:
7x = 259
Divide both sides by 7:
x = 37
Now that we know the value of x is 37, we can substitute it back into the equations to find the number of each coin.
Jacob has 3 times as many nickels as half dollars, so he has 3 * 37 = 111 nickels.
Jacob has 50 fewer quarters than nickels, so he has 111 - 50 = 61 quarters.
Therefore, Jacob has 61 quarters.