Question 421436
g = what greg weighs
k = what karen weighs
o = what olivia weighs


first statement is greg weighs 15 pounds less than twice what karen weighs.


this leads to the equation:


g = 2k - 15


second statement is olivia weighs 10 pounds more than karen.


this leads to the equation:


o = k + 10


third statement says their combined weight is at least 460 pounds.


this leads to the equation:


g + k + o >= 460


you have 3 equations to work with.


they are:


g = 2k - 15
o = k + 10
g + o + k >= 460


since you have values for g and o in terms of k, you can substitute in the third equation to get:


g + o + k >= 460 becomes:


2k - 15 + k + 10 + k >= 460


combine like terms to get:


4k - 5 >= 460


add 5 to both sides of the equation to get:


4k >= 465


divide both sides of the equation by 4 to get k >= 116.25


if we assume that k = 116.25, then we get:


we have k = 116.25
we also have g = 2k-15 = 232.5 - 15 = 217.5
we also have o = k + 10 = 126.25


we wind up with:


g = 217.5
o = 126.25
k = 116.25


add them up and we get g + o + k >= 217.5 + 126.25 + 116.25 = 460 which is true because it's the equal part of greater than or equal.


we also get g = 2k - 15 which becomes 217.5 = 2*116.25 - 15 = 232.5 - 15 = 217.5 which is true.


we also get o = k + 10 which becomes 126.25 = 116.25 + 10 = 126.25 which is true.


looks like all values are good.


assuming that karen weighs exactly 116.25 pounds, we have:


greg weighs 217.5 pounds
olivia weights 126.25 pounds
karen weighs 116.25 pounds


if k > 116.25, then the others go up in relation to that because of the equality in their relationships to k.


for example:


if k = 120 pounds, then:


g = 2k - 15 becomes g = 225


and:


o = k + 10 becomes o = 130


g + o + k would then be equal to 120 + 225 + 130 = 475 which is now the greater part of greater than or equal, and the equality relationships between g and k and o and k are still preserved.
g would be equal to 2 * k - 15 and o would be equal to k + 10.


bottom line is the statement that the sum of their weights is greater than or equal to 460 pounds throws a curve ball into the problem that makes it harder to visualize than if they has just said the sum of all 3 weights equals 460 pounds.


unless there was a specific reason for them to do so, i would assume that they meant equal to 460 pounds rather than greater than or equal to 460 pounds and solve the problem accordingly.


in that case, you would get:


k = 116.25 pounds
g = 217.5 pounds
o = 126.25 pounds