Keith has p pennies, n nickels, and d dimes in his pocket. The total number of coins is 9. The expression 0.01p+0.05n+0.10d0.01p+0.05n+0.10d represents the value of the coins, which is equal to $0.53. He has two fewer nickels than dimes. How many pennies does Keith have?
Keith has _____ pennies.
forget all those decimal points.
p+n+d = 9
p+5n+10d = 53
n = d-2
now just solve for p.
Nans
I don't know help
To find the number of pennies Keith has, we need to solve the given information and equations.
We are given that Keith has p pennies, n nickels, and d dimes. The total number of coins is 9, so we can write the equation:
p + n + d = 9 ...(1)
The expression 0.01p + 0.05n + 0.10d represents the value of the coins, which is equal to $0.53. Therefore, we can write the equation:
0.01p + 0.05n + 0.10d = 0.53 ...(2)
We are also given that Keith has two fewer nickels than dimes. So, we can write the equation:
n = d - 2 ...(3)
We now have three equations (1), (2), and (3) to solve. Let's solve them using the substitution method:
First, let's solve equation (3) for n and substitute it into equations (1) and (2):
n = d - 2 ...(3)
p + (d - 2) + d = 9 ...(1)
0.01p + 0.05(d - 2) + 0.10d = 0.53 ...(2)
Simplifying equation (1), we get:
p + 2d - 2 = 9 ...(4)
Simplifying equation (2), we get:
0.01p + 0.05d - 0.10 + 0.10d = 0.53
0.01p + 0.05d + 0.10d = 0.53 + 0.10
0.01p + 0.15d = 0.63 ...(5)
Now, let's isolate p in equation (4):
p = 9 - 2d + 2 ...(6)
Substituting equation (6) into equation (5):
0.01(9 - 2d + 2) + 0.15d = 0.63
0.09 - 0.02d + 0.02 + 0.15d = 0.63
-0.02d + 0.15d = 0.63 - 0.09 - 0.02
0.13d = 0.52
d = 0.52 / 0.13
d = 4
Now, substitute the value of d (4) into equation (6) to find p:
p = 9 - 2(4) + 2
p = 9 - 8 + 2
p = 3
Therefore, Keith has 3 pennies.
Keith has 3 pennies.