Solve a system of equations using augmented matrices word problems

Learning Objectives Identify two unknown quantities in a consumer math word problem. Organize given information and clues into a simple table (similar to an augmented matrix). Use relationships between unknown quantities to simplify a problem. Apply addition, subtraction, and simple division to solve for two unknown quantities. Check their solutions to ensure they fit all conditions of the word problem. Solve consumer math word problems involving two unknown items with a total and a relationship. Ever wonder how stores figure out prices when they have special deals on two different items? 🕵️‍♀️ Sometimes you know the total cost, but not the individual prices! In this lesson, you'll learn a super organized way, like using a special chart, to solve word problems that hav...

TermDefinitionExample Unknown QuantityA number or value that we need to find in a word problem. It's like a mystery number!If you buy apples and bananas, and you don't know the price of each, the price of an apple and the price of a banana are unknown quantities. ClueInformation given in a word problem that helps us figure out the unknown quantities. Clues are like hints!In a problem, 'The total cost was $10' is a clue. 'One item cost $2 more than the other' is another clue. Two-Part Problem (System of Equations)A word problem where you need to find two different unknown numbers, and you are given two or more clues that connect them. This is what mathematicians call a 'system of equations'.Finding the cost of a pencil AND an eraser when you know the...

Rule 1: Organize Your Information Create a special table (like an augmented matrix) to list the unknown items, their relationships, and the total amounts. This helps you see all the clues clearly and keep your numbers organized. Use columns like 'Item', 'Cost/Quantity', 'Relationship', and 'Total'. Rule 2: Balance the Clues If one item costs more than another, subtract that 'extra' amount from the total to find what the total would be if they cost the same. If one item costs less, you might add to make them equal. This step makes it easier to find the individual amounts by temporarily making the unknown parts equal in value or quantity. Rule 3: Divide to Find One Part $\text{New Total (after balancing)} \div \text{Numbe...