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Question 421436: I need help with this word problem please
Translate the following situation into an inequality:
Greg weighs fifteen pounds less than twice what Karen weighs and Olivia weighs ten pounds more than Karen, their combined weight is at least 460 pounds. How much do they each weigh?
I started with:
15<2+10=460
but I know I'm way off with this.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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
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