A student scored 75 and 92 on some tests. Write and solve an inequality to find values for the third test score that would give her an average between 80 and 90 inclusive
Let's call the third test score "x".
To find the average of the three test scores, we need to add up the scores and divide by 3.
The average between 80 and 90 inclusive is between 80 and 90, so we can write the inequality as:
80 ≤ (75 + 92 + x)/3 ≤ 90
Now let's solve for x:
80 ≤ (75 + 92 + x)/3 ≤ 90
Multiply both sides of the inequality by 3:
240 ≤ 75 + 92 + x ≤ 270
Combine like terms:
240 ≤ 167 + x ≤ 270
Subtract 167 from all sides:
240 - 167 ≤ 167 - 167 + x ≤ 270 - 167
73 ≤ x ≤ 103
So the values for the third test score that would give her an average between 80 and 90 inclusive are any values between 73 and 103.
Mo is selling key chains as a fundraiser. If their goal is to raise at least $135, how many key chains must they sell at $1.50 each to meet that goal?
Let's denote the number of key chains Mo must sell as "x".
Since each key chain is sold for $1.50, the total amount of money raised by selling "x" key chains can be calculated as 1.50x dollars.
According to the problem, the goal is to raise at least $135. Therefore, we can write the inequality:
1.50x ≥ 135
To find the minimum number of key chains that Mo must sell, we need to solve this inequality for "x".
Divide both sides of the inequality by 1.50:
x ≥ 135 / 1.50
Simplifying the right side of the inequality:
x ≥ 90
Thus, Mo must sell at least 90 key chains in order to meet their goal of raising $135 or more.
To find the range of values for the third test score, we can set up an inequality.
Let x represent the third test score.
The average score is given by the formula:
Average = (Sum of scores) / (Number of scores)
In this case, the sum of the three tests is 75 + 92 + x, and the number of scores is 3.
We can replace these values in the average formula:
80 ≤ (75 + 92 + x) / 3 ≤ 90
To solve the inequality, we can multiply each term in the inequality by 3 to eliminate the fraction:
240 ≤ 75 + 92 + x ≤ 270
Next, we can simplify the inequality:
240 ≤ 167 + x ≤ 270
Subtracting 167 from each term:
73 ≤ x ≤ 103
Therefore, the third test score must be between 73 and 103 (inclusive) in order to have an average score between 80 and 90 (inclusive).
To find the values for the third test score that would give the student an average between 80 and 90, we can set up an inequality.
Let's denote the third test score as x.
To find the average of three numbers, we sum them and divide by 3. In this case, the sum of the three test scores (x, 75, and 92) divided by 3 should be between 80 and 90 inclusive.
So, we can write the inequality as:
(75 + 92 + x) / 3 ≥ 80 and (75 + 92 + x) / 3 ≤ 90
Now, let's solve the inequality step by step.
(75 + 92 + x) / 3 ≥ 80
Multiply both sides of the inequality by 3 to eliminate the fraction:
75 + 92 + x ≥ 240
Combine like terms:
167 + x ≥ 240
Subtract 167 from both sides:
x ≥ 240 - 167
Simplifying:
x ≥ 73
Now let's solve the second part of the inequality:
(75 + 92 + x) / 3 ≤ 90
Multiply both sides of the inequality by 3:
75 + 92 + x ≤ 270
Combine like terms:
167 + x ≤ 270
Subtract 167 from both sides:
x ≤ 270 - 167
Simplifying:
x ≤ 103
So, the values for the third test score (x) that would give the student an average between 80 and 90 inclusive are between 73 and 103 (both inclusive).