SOLUTION: Define two variables and translate the sentence into an inequality. The costs are at least$ 29,000 under the revenues. Let x=costs and let y=revenues

Question 1182102: Define two variables and translate the sentence into an inequality.
The costs are at least$ 29,000 under the revenues.
Let x=costs and let y=revenues

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

In my opinion, the given statement can be interpreted to mean two different ways, leading to inequalities that say the exactly opposite things.

(1) Strict mathematical interpretation....

x = costs
y = revenue
y-29000 = $29,000 under revenues

"A at least B" means A is greater than or equal to B:
"costs are at least $29,000 under revenues" --> x is greater than or equal to y-29000 --> x >= y-29000 [1]

(2) interpreting the English phrase....

"costs are at least $29,000 under revenue" --> "the difference between costs and revenue is at least $29,000"

y-x >= 29000 [2]

Inequality [2] says the difference between revenue and costs is greater than or equal to $29000.

But writing inequality [1] as revenue in terms of cost...

x >= y-29000
x+29000 >= y
y <= x+29000
y-x <= 29000

That says the difference between revenue and costs is LESS THAN or equal to $29,000.

Since two valid interpretations of the given statement lead to opposite answers, the conclusion to be drawn is that the wording of the statement is deficient.

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