Answers
there must be at least 2 boxes of fudge containing nuts at the fudge shop on Monday morning.The scenario states that the total amount of fudge containing nuts on Monday afternoon is at least 29(5/8) pounds. So, we can write the inequality:x + 12(3/4) ≥ 29(5/8)
How to solve the question?
(a) Let's define "x" as the amount of fudge containing nuts that was at the fudge shop on Monday morning. Since three-fourths of the fudge contains nuts, we can say that:
x = (3/4)total fudge at the fudge shop on Monday morning
Then, Helena prepares an additional 12(3/4) pounds of fudge containing nuts. Therefore, the total amount of fudge containing nuts on Monday afternoon is:
x + 12(3/4)
The scenario states that the total amount of fudge containing nuts on Monday afternoon is at least 29(5/8) pounds. So, we can write the inequality:
x + 12(3/4) ≥ 29(5/8)
(b) Let's first convert the mixed number 12(3/4) into an improper fraction:
12(3/4) = (4*12 + 3)/4 = 51/4
Similarly, we can convert the mixed number 29(5/8) into an improper fraction:
29(5/8) = (8*29 + 5)/8 = 233/8
Now, we can substitute these values into the inequality we wrote in part (a):
x + 51/4 ≥ 233/8
To solve for x, we need to isolate it on one side of the inequality. Let's start by subtracting 51/4 from both sides:
x ≥ 233/8 - 51/4
x ≥ 10/8
Simplifying the right-hand side:
x ≥ 5/4
Therefore, the inequality that represents the scenario is:
(3/4)total fudge at the fudge shop on Monday morning + 12(3/4) ≥ 29(5/8)
And the solution to this inequality is:
x ≥ 5/4
(c) Since fudge is packaged into 1-pound boxes, the fewest number of boxes of fudge at the fudge shop on Monday morning is equal to the amount of fudge containing nuts on Monday morning, which is "x". From part (b), we know that:
x ≥ 5/4
The smallest whole number that is greater than or equal to 5/4 is 2. Therefore, there must be at least 2 boxes of fudge containing nuts at the fudge shop on Monday morning.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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Sunday
Monday
Tuesday Wednesday Thursday
Friday
Saturday
Temperature
49
(degrees F)
55
52
46
47
42
38
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have a great day/night and crush that homework/class!! ur loved