WORD PROBLEMS TO EXPRESSIONS
Learn to turn real-life situations into algebraic expressions! Study the examples carefully.
Many real-life situations involve fixed amounts (constants) and changing amounts (variables). Your job is to identify which is which, then write the correct algebraic expression.
"Per" and "each" mean multiply the rate by the variable.
"Plus" and "and" (for cost) mean add the parts together.
"Times as many" means multiply the quantity by that number.
For geometry: Perimeter = 2(length + width), Area = length × width
Common Mistakes: Don't multiply the fixed fee by the variable! A flat charge like "₱40" stays as 40, not 40x. Only the "per unit" part gets multiplied.
Scenario: A parking lot charges a flat rate of ₱40 for entry, then ₱20 for each additional hour (h).
Step 1 (Fixed): The entry fee is always ₱40. → 40
Step 2 (Variable): ₱20 per hour means 20 × h. → 20h
Step 3 (Combine): Add them together. → 40 + 20h
Final Expression: 40 + 20h
Scenario: A student buys x notebooks at ₱15 each and y pens at ₱8 each.
Step 1 (Notebooks): 15 per notebook × x notebooks. → 15x
Step 2 (Pens): 8 per pen × y pens. → 8y
Step 3 (Combine): Add the costs. → 15x + 8y
Final Expression: 15x + 8y
Scenario: A water tank has 50 liters. If x liters are used each hour for 3 hours, how many liters remain?
Step 1 (Used): x liters per hour × 3 hours. → 3x
Step 2 (Remaining): Subtract the used amount from the initial 50. → 50 - 3x
Final Expression: 50 - 3x
Scenario: The width of a rectangle is w. Its length is 3 times the width.
Step 1 (Length): 3 times w. → 3w
Step 2 (Area Formula): Area = length × width. → (3w) × (w)
Step 3 (Simplify): 3 × w × w = 3w². → 3w²
Final Expression: 3w²
Scenario: A vendor earns ₱200 per day plus a commission of ₱30 for each item sold (s).
Step 1 (Base): Fixed daily earn is ₱200. → 200
Step 2 (Commission): ₱30 per item × s items. → 30s
Step 3 (Combine): Add base and commission. → 200 + 30s
Final Expression: 200 + 30s
Scenario: A jeepney fare is ₱12 for the first 4 km, then ₱2 for each additional kilometer (k).
Step 1 (Base Fare): The first 4 km is a fixed ₱12. → 12
Step 2 (Variable): ₱2 per km × k kilometers. → 2k
Step 3 (Combine): Add base fare and variable fare. → 12 + 2k
Final Expression: 12 + 2k
Tip: Always ask yourself — "What stays the same?" (constant) and "What changes?" (variable × rate). Then combine them!
Seatwork Time!
Read each situation carefully. Choose the correct algebraic expression!
Mathemalupit | Interactive Math Review & Seatwork