Marie, Brenda, and Deepa all went for a run. Marie ran twice as far as Brenda, and Deepa ran 3 km less than Marie. Together, they ran a combined distance of 22 km. How far did each person run?
we can make a system of equations for this one. but first, let's define some variables for Marie, Brenda, and Deepa: m, b, and d, respectively.
here is our system of equations:
m = 2b, or b = m/2
d = m - 3
d + m + b = 22
in the first two equations, you can see that they both can be written in terms of Marie's run distance. now we can use subtitution and substitute those expressions into the last equation.
m - 3 + m + m/2 = 22
2m + m/2 = 25
4m/2 + m/2 = 25
5m = 50
m = 10
now to solve for the others, we can simply plug back our value of m into the previous equations.
d = 10 - 3 = 7.
b = 10/2 = 5.
hope this helped! please let me know if you are confused about anything i did