Jake winters plans to invest $7,400 find the interest rate required for the fun to grow to $7,844 and 8 months

log(1 + rate) = {log(total) -log(Principal)} ÷ Years
total = 7.844   principal = 7,400  Years = .6666666

log(1 + rate) = {log(7,844) -log(7,400)} / .6666666
log(1 + rate) = {3.894537585 -3.8692317197} / .6666666
log(1 + rate) = 0.0253058653 / .6666666
log(1 + rate) = 0.0379588017

Now we  raise 10 to the power of 0.0379588017
10^0.0379588017 = 1.0913368046
which is 1 + the rate
rate = .0913368046 which equals
9.13368046 %

Source:
http://www.1728.org/compint2.htm

15 hamburgers were sold and 30 hotdogs were sold.

The systems of equations are x + y = 45 and 4x + 5y = 195.

Step-by-step explanation:

Let's make two equations.

x + y = 45

This represents the total of hotdogs and hamburgers sold

4x + 5y = 195

This represents the amount of money made for each food.

These are systems of equations, when you use 2 equations to solve a problem. I will use the strategy, Elimination for the following systems of equations. Anyways the goal is to multiply a number to x + y = 45 to cancel out one of the variables in 4x + 5y = 195. In other words, when we add these equations, the sum of the xs or ys will equal 0.

Let's multiply -5 to both x and y.

Now we have -5x -5y = -225 + 4x + 5y= 195

We will end up with -x = -30. This means that x = 30.

Now that we know x = 30, we can plug in 30 as x in one of the equations. I will plug in 30 into x + y = 45. 30 + y = 45.

Solve for y in 30 + y = 45, so y=15.

This means 15 hamburgers were sold and 30 hotdogs were sold.