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?
$22.50 and $2.00 for #4???
To write the inequalities for the given problems, we need to understand the relationships between the numbers given in the problem statements. Let's go through each problem and write the corresponding inequalities without solving them:
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?
Let's consider the lowest grade as x. To maintain at least an 18 average, the sum of all the grades divided by the total number of grades should be greater than or equal to 18. So we can write the inequality as:
(19 + 17 + 20 + 15 + x) / 5 ≥ 18
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?
Let's assume Luis worked for L hours. Since Stacey worked 4 more hours than Luis, we can represent Stacey's hours as L + 4. The sum of their hours should be greater than 28, so we can write the inequality as:
L + (L + 4) > 28
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?
Let's assume the younger son saves Y dollars. Since the older one agrees to save twice as much, the older son will save 2Y dollars. The sum of their savings should be greater than $45, so we can write the inequality as:
Y + 2Y > 45
Now, let's solve the inequalities to find the actual values for each problem:
2. (19 + 17 + 20 + 15 + x) / 5 ≥ 18
Solve for x by multiplying both sides by 5:
19 + 17 + 20 + 15 + x ≥ 90
x ≥ 90 - (19 + 17 + 20 + 15)
x ≥ 90 - 71
x ≥ 19
3. L + (L + 4) > 28
Simplify the equation:
2L + 4 > 28
2L > 28 - 4
2L > 24
L > 12
4. Y + 2Y > 45
Simplify the equation:
3Y > 45
Y > 45 / 3
Y > 15
Therefore, the correct values for each problem are:
2. The lowest grade you can receive on the next quiz and maintain at least an 18 average is 19 or any number greater than 19.
3. The least number of hours each worked is Luis ≥ 12 hours and Stacey ≥ 16 hours.
4. The amount each must save is the younger son saving Y > $15 and the older son saving 2Y > $30.