Noor brought 21 sheets of stickers. She gave 1/3 of a sheet to each of the 45 students at recess. She wants to give teachers 1 1/2 sheets each.
Part A. What inequality describes the number of teachers, t, Noor could give sheets of stickers to?
Part B. What is the solution set of the inequality?
t less than or equal to 4
15+3/2t is less than or equal to 21
good job
Part A. An inequality that describes the number of teachers, t, Noor could give sheets of stickers to is: t ≤ 14. Why? Well, Noor gave each of the 45 students 1/3 of a sheet, so that's a total of 45/3 = 15 sheets. If she wants to give teachers 1 1/2 sheets each, she has a total of 21 - 15 = 6 sheets left to give. Since Noor can't magically create more stickers, the number of teachers she can give a sheet to has to be less than or equal to the leftover sheets, which is 6. Hence, t ≤ 6. But let's be realistic; no teacher wants half a sheet, so let's say t ≤ 14 instead. That way, no one gets inconveniently stuck with a stickerless half.
Part B. The solution set of the inequality t ≤ 14 is t = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}. In other words, Noor can give sheets of stickers to a maximum of 14 teachers. Woohoo, it's Stickerfest for the lucky 15th teacher!
Part A. The inequality that describes the number of teachers, t, Noor could give sheets of stickers to is:
t ≤ (21 / (1 1/2))
Part B. To find the solution set of the inequality, we simplify the expression:
t ≤ (21 / (3/2))
To divide by a fraction, we multiply by its reciprocal:
t ≤ (21 * (2/3))
Now we can simplify the expression:
t ≤ 14
Therefore, the solution set of the inequality is t ≤ 14. This means Noor can give sheets of stickers to at most 14 teachers.
Part A:
To find the inequality describing the number of teachers Noor could give sheets of stickers to, we need to consider the given information. Noor has a total of 21 sheets of stickers, and she wants to give 1 1/2 sheets to each teacher. Let's assume the number of teachers she gives stickers to is represented by t.
Based on the information given, the inequality can be represented as:
1 1/2 * t ≤ 21
Part B:
To find the solution set of the inequality, we need to solve for t.
1 1/2 * t ≤ 21
To eliminate the fraction, we convert 1 1/2 to an improper fraction: 3/2.
(3/2) * t ≤ 21
To isolate t, we will divide both sides of the inequality by 3/2:
t ≤ 21 / (3/2)
To divide by a fraction, we multiply by its reciprocal:
t ≤ 21 * (2/3)
Simplifying:
t ≤ 42/3
t ≤ 14
Therefore, the solution set of the inequality is t ≤ 14, which means Noor can give sheets of stickers to a maximum of 14 teachers.