Molly scored 150 and 175 points on her first two rounds of Candy Crush. Write and solve a compound inequality to find the possible values for a third game that would give her an average between 160 and 170.
Let's call the score of the third game x. To find the average between 160 and 170, we can set up the following compound inequality:
160 ≤ (150 + 175 + x)/3 ≤ 170
First, let's simplify the middle expression:
325 + x ≤ 510
Now, solve for x:
x ≤ 510 - 325
x ≤ 185
So, Molly would need to score a third game with a value of x less than or equal to 185 to have an average between 160 and 170.
To find the possible values for a third game that would give Molly an average between 160 and 170, we need to calculate the sum of her first two scores and divide it by 3 (since there are three games in total).
Let's represent the third game score as "x".
The sum of her first two scores is: 150 + 175 = 325.
The average of three games is: 325 + x / 3.
To ensure that Molly's average falls between 160 and 170, we can write the following compound inequality:
160 ≤ (325 + x) / 3 ≤ 170.
To solve this compound inequality, we can begin by multiplying all terms by 3 to eliminate the fraction:
3 * 160 ≤ 325 + x ≤ 3 * 170,
480 ≤ 325 + x ≤ 510.
Next, we can subtract 325 from all parts of the inequality to isolate the variable x:
480 - 325 ≤ x ≤ 510 - 325,
155 ≤ x ≤ 185.
Therefore, the possible values for the third game that would give Molly an average between 160 and 170 are any value between 155 and 185, inclusive.
To write and solve a compound inequality, we need to first determine the average score Molly needs to achieve in her third game.
The average score between 160 and 170 can be calculated as the sum of the two extremes divided by 2: (160 + 170) / 2 = 330 / 2 = 165.
Let's denote the score in her third game as "x". We can write the compound inequality as follows:
160 <= (150 + 175 + x) / 3 <= 170.
To solve this compound inequality, we will first simplify it by multiplying all parts by 3 to eliminate the fraction:
3 * 160 <= 150 + 175 + x <= 3 * 170.
This simplifies to:
480 <= 325 + x <= 510.
Next, we will subtract 325 from all parts of the inequality:
480 - 325 <= 325 + x - 325 <= 510 - 325.
This simplifies to:
155 <= x <= 185.
Therefore, the possible values for Molly's score in her third game that would give her an average between 160 and 170 are between 155 and 185 (inclusive).