Scenario: Budget & Grade Planning - Learn to solve inequalities and represent solutions on number lines!
Sarah has taken 3 tests with scores of 82, 78, and 85. She needs an average of at least 85 to get an A in the class. What score does she need on the fourth test?
Setting up the inequality:
Average = (82 + 78 + 85 + x) ÷ 4
(82 + 78 + 85 + x) ÷ 4 ≥ 85
Step 1: Simplify the numerator
(245 + x) ÷ 4 ≥ 85
Step 2: Multiply both sides by 4
245 + x ≥ 340
Step 3: Subtract 245 from both sides
x ≥ 95
Answer: Sarah needs at least 95 on the fourth test.
Number Line:
The filled circle at 95 means "include 95", and the arrow shows "all numbers greater than or equal to 95".
< (less than)
> (greater than)
Use open circles on number line
≤ (less than or equal to)
≥ (greater than or equal to)
Use filled circles on number line
Tom has a budget of $200 for school supplies. He has already spent $85. He wants to buy notebooks that cost $3 each. How many notebooks can he afford?
Setting up the inequality:
Amount spent + (Cost per notebook × Number of notebooks) ≤ Budget
85 + 3x ≤ 200
Step 1: Subtract 85 from both sides
3x ≤ 115
Step 2: Divide both sides by 3
x ≤ 38.33...
Answer: Tom can afford at most 38 notebooks (since he can't buy a fraction of a notebook).
Solve: 2x - 5 < 11
Your solution:
A student has scores of 88, 92, and 85. What score is needed on the fourth test to have an average of at least 90?
Your calculation: