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.