Bob has 19 coins totaling $1.50. If he only has dimes and nickels, how many of each coin does he have?
see related questions below, or the coin problems posted after this one.
To find the number of nickels and dimes Bob has, we can set up a system of equations based on the information given:
Let's assume Bob has x nickels and y dimes.
From the given information, we know two things:
1. Bob has a total of 19 coins.
So, the equation would be: x + y = 19
2. The total value of his coins is $1.50.
Since each nickel is worth $0.05 and each dime is worth $0.10, we can write the equation: 0.05x + 0.10y = 1.50
Now, we have a system of equations:
x + y = 19 ---(Equation 1)
0.05x + 0.10y = 1.50 ---(Equation 2)
There are different methods to solve this system of equations, but let's use a method called substitution.
1. Solve Equation 1 for x:
x = 19 - y
2. Substitute x in Equation 2 with 19 - y:
0.05(19 - y) + 0.10y = 1.50
Now, let's simplify and solve for y:
0.95 - 0.05y + 0.10y = 1.50
0.05y + 0.10y = 1.50 - 0.95
0.15y = 0.55
Divide both sides by 0.15 to isolate y:
y = 0.55 / 0.15
y = 3.67
Since we cannot have a fraction of a coin, we round y down to the nearest whole number:
y ≈ 3
Now substitute y = 3 back into Equation 1 to find x:
x + 3 = 19
x = 19 - 3
x = 16
So, Bob has 3 dimes and 16 nickels.