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Question 694772: What is a possible value of y such that 30% of y ≤ 300 ≤ 40% of y?
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! It would be beneficial if we converted percentage over to decimals in order to get a clearer picture of what we are dealing with. If you remember, percent roughly means "out of one hundred," so 30% is 30/100 or 0.3 and 40% is 40/100 or 0.4. The word "of" in math generally means the same as multiplication. Converting our equation we have:
30% of y ≤ 300 ≤ 40% of y = 0.3y ≤ 300 ≤ 0.4y.
Now we would just solve like any compound inequality:
0.3y ≤ 300 ≤ 0.4y
0.3y ≤ 300 and 300 ≤ 0.4y
y ≤ 1000 and 750 ≤ y (divide each side by 0.3 and 0.4 respectively)
750 ≤ y ≤ 1000 (this is the two above answers put into a compound inequality).
So, we have our compound inequality 750 ≤ y ≤ 1000 that satisfies the conditions of 0.3y ≤ 300 ≤ 0.4y. Any number between and including 750 and 1000 would make this compound inequality true.
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