Solve proportions: word problems
Key notes :-
1️⃣ What is a Proportion?
A proportion is an equation that shows two ratios are equal.
🔹 Example:
a/b = c/d
✅ Means: a:b = c:d
2️⃣ How to Solve Proportions
Set up the proportion from the word problem 📝
Use cross-multiplication to find the unknown 🔄
a:b = c:x ⟹ a⋅x = b⋅c
Solve for the unknown number ✏️
Check your answer by substituting it back ✅
3️⃣ Steps for Word Problems
- Read carefully 📖 – Identify what is known and what you need.
- Assign variables ✍️ – Let xxx be the unknown.
- Write a ratio or fraction 🔢 – Match quantities correctly.
- Set up the proportion ⚖️ – Make the ratios equal.
- Solve using cross-multiplication ✖️➗
- Answer with correct units 🏷️
4️⃣ Tips & Tricks
- Keep units consistent (kg, m, liters…) ⚖️
- Check if the proportion makes logical sense 💡
- For percent problems, convert % to fractions first 🔢
- Always simplify fractions if possible ✨
5️⃣ Example Problem
Problem:
A recipe needs 3 cups of sugar for 4 cups of flour. How much sugar is needed for 10 cups of flour? 🍰
Solution:
3/4 = x/10
Cross multiply:
4x = 30 ⟹ x = 7.5
✅ Answer: 7.5 cups of sugar
6️⃣ Fun Emoji Reminder
- Ratios: 🔹🔸
- Unknown: ❓
- Cross Multiply: ✖️
- Check Answer: ✅
- Units: 🏷️
Learn with an example
🔔 Jonah prepared 4 kilograms of dough after working 2 hours. How much dough did Jonah prepare if he worked for 7 hours? Assume the relationship is directly proportional.
______ kilograms
Set up a proportion and solve for n.
4 kilograms / 2 hours = n kilograms / 7 hours
4/2 ( 2 . 7 ) = n/7 ( 2 . 7 ) Multiply both sides by 2 · 7
4 · 7 = 2n Simplify
28 = 2n Multiply
14 = n Divide both sides by 2
If Jonah worked for 7 hours, he prepared 14 kilograms of dough.
🔔 Ronald spent 8 minutes on the phone while routeing 4 phone calls. In all, how many phone calls does Ronald have to route to spend a total of 14 minutes on the phone? Assume the relationship is directly proportional.
______ phone calls
Set up a proportion and solve for n.
8 minutes / 4 phone calls = 14 minutes / n phone calls
8/4 ( 4n ) = 14/n ( 4n ) Multiply both sides by 4n
8n = 14 · 4 Simplify
8n = 56 Multiply
n = 7 Divide both sides by 8
To spend a total of 14 minutes on the phone, Ronald has to route 7 phone calls.
🔔 Rodrigo prepared 4 kilograms of dough after working 2 hours. How much dough did Rodrigo prepare if he worked for 8 hours? Assume the relationship is directly proportional.
____ kilograms
Set up a proportion and solve for n.
4 kilograms / 2 hours = n kilograms / 8hours
4/2 (2 . 8) = n/8 (2 . 8) Multiply both sides by 2 · 8
4 · 8 = 2n Simplify
32 = 2n Multiply
16 = n Divide both sides by 2
If Rodrigo worked for 8 hours, he prepared 16 kilograms of dough.
Let’s Practice!
