Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type does she have
5 N + 10 D = 350
N + D = 50
Solve that pair of equations for N and D, the number of nickels and dimes.
10,11 and 12
To find out how many nickels and dimes Jill has, we can set up a system of equations based on the given information.
Let's assume Jill has x nickels and y dimes.
1. The total value of the nickels is 5 cents each, so the value of x nickels is 5x cents.
2. The total value of the dimes is 10 cents each, so the value of y dimes is 10y cents.
According to the problem, Jill has 50 coins in total, so we can write the following equation:
x + y = 50 (Equation 1)
The total value of Jill's coins, in cents, is given as $3.50, which can be written as 350 cents. Therefore, we can set up another equation:
5x + 10y = 350 (Equation 2)
Now we have a system of equations:
x + y = 50 (Equation 1)
5x + 10y = 350 (Equation 2)
To solve this system, we can use the method of substitution or elimination. Let's solve using substitution:
From Equation 1, we can isolate x:
x = 50 - y
Substitute this value of x into Equation 2:
5(50 - y) + 10y = 350
250 - 5y + 10y = 350
250 + 5y = 350
5y = 350 - 250
5y = 100
y = 100/5
y = 20
Substituting this value of y back into Equation 1, we can find x:
x + 20 = 50
x = 50 - 20
x = 30
Therefore, Jill has 30 nickels and 20 dimes.