SOLUTION: Please help me solve this Finite Math problem! a consumer set out to compare prices on premiums of comparable insurance policies offered by three companies: Country Farm, Metma,

Question 1116885: Please help me solve this Finite Math problem!
a consumer set out to compare prices on premiums of comparable insurance policies offered by three companies: Country Farm, Metma, and Wisely. She found that Country Farm was $35 higher than Metma but $25 lower than Wisely. Wisely was $155 less than the sum of the premiums of the other two. Find the premium charged by each company
Found 2 solutions by Theo, solver91311:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

and

And

Substitute

You can figure the other two by yourself

John

My calculator said it, I believe it, that settles it

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