a jar contains $1.51 in pennies, nickels, and dimes. There are 4 more pennies then there are dimes and there are twice as many nickels as there are dimes...how many of each coins are in the jar
A minor league baseball team plas 84 games in a season. If the team won 15 more than twice as many games as they lost, how many wins and losses did the team have?
do not know
To solve this problem, we can set up a system of equations. Let's define variables for the number of pennies, nickels, and dimes in the jar.
Let's say:
P = number of pennies
N = number of nickels
D = number of dimes
According to the problem, we have three pieces of information:
1. There are 4 more pennies than dimes, so we can write this as an equation: P = D + 4.
2. There are twice as many nickels as dimes, so we can write this as an equation: N = 2D.
3. The total value of the coins in the jar is $1.51. To find the total value, we need to know the value of each type of coin. A penny is worth $0.01, a nickel is worth $0.05, and a dime is worth $0.10. So, the equation representing the total value is: 0.01P + 0.05N + 0.10D = 1.51.
Now we have a system of three equations:
P = D + 4
N = 2D
0.01P + 0.05N + 0.10D = 1.51
To solve this system of equations, we can substitute the second equation (N = 2D) into the other equations.
Substituting N = 2D into the first equation P = D + 4, we get:
2D = D + 4
D = 4.
So, there are 4 dimes in the jar.
Substituting N = 2D into the third equation 0.01P + 0.05N + 0.10D = 1.51, we get:
0.01P + 0.05(2D) + 0.10D = 1.51
0.01P + 0.1D + 0.10D = 1.51
0.01P + 0.20D = 1.51
0.01P = 1.51 - 0.20D.
We know that P = D + 4, so substitute this value into the equation:
0.01(D + 4) = 1.51 - 0.20D
0.01D + 0.04 = 1.51 - 0.20D
0.01D + 0.20D = 1.51 - 0.04
0.21D = 1.47
D = 1.47 / 0.21
D ≈ 7.
So, there are approximately 7 dimes in the jar.
Now that we know the values of D (7), we can find the values of P (pennies) and N (nickels) using the equations:
P = D + 4
N = 2D.
P = 7 + 4
P = 11.
N = 2 * 7
N = 14.
To summarize, there are 11 pennies, 14 nickels, and 7 dimes in the jar.