This a problem of two equations in two variables. The first step in solving the problem is defining the variables. I will define them as follows:

x = Amount of money invested at 4 percent

y = Amount of money invested at 7 percent

Now we need to write two equations using the two variables.

The amount invested at 4 percent (x) plus (+) the amount invested at 7 percent (y) equals (=) 41,000.

x + y = 41,000 Equation 1

The amount of interest from the money invested at 4 percent (.04x) plus (+) the amount of interest from the money invested at 7 percent (.07y) equals (=) 1940.

.04x + .07y = 1940 Equation 2

You can use either substitution or elimination method to solve. I am going to use substitution.

x + y = 41,000 Equation 1

x + y - y = 41,000 - y Subtract y from each side

x = 41,000 - y Simplify

.04x + .07y = 1940 Equation 2

.04(41,000 - y) + .07y = 1940 Substitution (value of x from equation 1)

1640 - .04y + .07y = 1940 Distribute the .04

1640 + .03y = 1940 Simplify

1640 + .03y - 1640 = 1940 - 1640 Subtract 1640 from each side

.03y = 300 Simplify

.03y/.03 = 300/.03 Divide each side by .03

y = 10,000 Simplify

x = 41,000 - y Equation 1 solved for x

x = 41,000 - 10,000 Substitution

x = 31,000 Simplify

Phyllis invested $31,000 at 4% and $10,000 at 7%.