Question 1116885
let c = premium charged by country farm.
let m = premium charged by metma.
let w = premium charged by wisely.


country farm charges 35 more than metma, therefore c = m + 35


country farm charges 25 less than wisely, therefore c = w - 25


wisely charges 155 less than the sum of the premiums of country farm and metma, therefore w = c + m - 155


you have 3 equations that need to be solved simultaneously.,


they are:


c = m + 35 (first original equation)
c = w - 25 (second original equation)
w = c + m - 155 (third original equation)


rearrange the terms in each equation so that the variables are on the left and the constants are on the right.


the equations become:


c - m = 35
c - w = -25
w - c - m = -155


subtract the second equation from the first to get -m + w = 60


rearrange the terms to get w - m = 60


subtract this equation from the third equation of w - c - m = -155 to get -c = -215


solve for c to get c = 215


in the equation of c = m + 35, replace c with 215 to get:


215 = m + 35


solve for m to get m = 180


you now have m = 180 and c = 215.


replace m and c in the third original equation to get:


w = c + m - 155 becomes w = 215 + 180 - 155


solve for w to get w = 240


you now have:


c = 215
m = 180
w = 240


go back to your original 3 equations and replace c and m and w with their respective values to see if those equations are all true.


your 3 original equations are:


c = m + 35
c = w - 25
w = c + m - 155


these become:


215 = 180 + 35, which is true.
215 = 240 - 25, which is true.
240 = 215 + 180 - 155, which is true.


all 3 original equations are true, therefore the solution looks good.


looks like:


country farms premium is 215.
metma premium is 180.
wisely premium is 240.