let

p = the number of pennies, p>0

n = number of nickles, n>0

1 penny = 1 cent

1 nickle = 5 cents

Manuel has pennies and nickels with a total value of $1.15 = 115 cents:

1*p + 5*n = 115

The number of nickels is 43 less than the number of pennies:

n = p - 43

by solving the system of equations:

1*p + 5*n = 115

n = p - 43

we find:

p = 55 pennies

n = 22 nickles

click here to see the step by step solution of the system of equations:

Manuel has 55 pennies.