Linear Equation Word Problems
Step 2: There should be one such quantity which you need to find. Represent that quantity in terms of a variable.
Step 3: Relate all other unknown quantities in terms of the variable assumed in step 2.
Step 4: Form an equation according to the information in question.
Step 5: Solve the equations to find the value of variables.
Example: The sum of three consecutive even numbers is 78. What is the smallest of these numbers?
Let us assume that the three consecutive even numbers are x, x + 2, and x + 4.
x + x + 2 + x + 4 = 78
3x + 6 = 78
3x = 72 implies x = 24
Check your answer: x + (x + 2) + (x + 4) = 24 + (24 + 2) + (24 + 4) = 24 + 26 + 28 = 78
Example: If the difference between two numbers is 38, and the ratio of two numbers is 6:5. Find the numbers.
Let the numbers be x and y.
Then x – y = 38 … Equation (1)
x : y = 6 : 5 … Equation (2)
From equation (1), x = 38 + y
Equation (2) implies => 5x = 6y
Put x = 38 + y in 5x = 6y Þ 5(38 + y) = 6y
228 + 5y = 6y implies y = 228
x = 38 + 228 = 266
The numbers are 228 and 266.
- Denise bought a magazine for $2 and some notepads for $3 each. She spent a total of $11. How many notepads did she buy?
- For a field trip 28 students rode in cars and the rest filled six buses. How many students were in each bus if 232 students were on the trip?
- Joe’s bikes rents bikes for $15 plus $8 per hour. Julia paid $47 to rent a bike. For how many hours did she rent the bike?
- Shelly had $24 to spend on five pencils. After buying them, she is left with $14. How much did each pencil cost?
- Ted sold half of his comic books and then bought 15 more. He now has 45. With how many did he begin?
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