Directions:Write inequalities for the numbers 2 - 4 below. Do not solve them!
Problems:
2.Your quiz grades are 19, 17, 20, and 15. What is the lowest grade you can receive on the next quiz and maintain at least an 18 average?
3.Stacey and Luis volunteer at the local hospital. Stacey worked 4 more hours than Luis, and together they worked more than 28 hours. What is the least number of hours each worked?
4.Mrs. Culpepper has promised her two sons that they may go to a concert if together they save more than $45. The older son agrees to save twice as much as the younger one. How much must each save?
I will give you some help.
2. The average/mean is all the scores added together and divided by the number of scores.
(19 + 17 + 20 + 15 + X)/5 ≥ 18
Treating the inequality just like an equation, calculate X for the lowest score that can be obtained.
3. Let X = Lius' hours and X + 4 = Stacy's. Adding them gives you at least 28. Using the appropriate formula should give you the answer.
4. Let X = younger son's savings, which means that the older son saves 2X. As with the previous two problems, construct the formula and solve for X and 2X. Do you understand why I designated the savings as I did?
I hope this helps a little more. Thanks for asking.
2. Let X be the lowest grade on the next quiz.
(19 + 17 + 20 + 15 + X)/5 ≥ 18
3. Let X = Luis' hours and X + 4 = Stacey's hours.
X + (X + 4) > 28
4. Let X = younger son's savings and 2X = older son's savings.
X + 2X > 45
2. Let X represent the lowest grade you can receive on the next quiz.
The average of all the quiz grades is calculated by adding them together and dividing by the number of scores. In this case, the average is at least 18.
So, (19 + 17 + 20 + 15 + X)/5 ≥ 18
This inequality represents the condition that the average of the quiz grades should be at least 18. To find the lowest grade you can receive, you solve this inequality for X.
3. Let X represent Luis' hours and X + 4 represent Stacey's hours.
The problem states that Stacey worked 4 more hours than Luis, and together they worked more than 28 hours.
So, X + (X + 4) > 28
This inequality represents the condition that the total number of hours they worked should be more than 28.
4. Let X represent the younger son's savings. According to the problem, the older son saves twice as much as the younger one.
So, the older son's savings would be 2X.
The problem also states that the total savings of both sons should be more than $45.
So, X + 2X > 45
This inequality represents the condition that the total savings should be more than $45.
By setting up and solving these inequalities, you can find the values that satisfy the given conditions. However, it is important to note that the inequalities alone do not provide the exact answers to the problems. They serve as a framework to find the possible solutions.