Mathematics
Grade 5
15 min
Solve a system of equations using augmented matrices
Solve a system of equations using augmented matrices
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1
Introduction & Learning Objectives
Learning Objectives
Organize information from consumer math word problems into a structured table.
Identify two unknown quantities (mystery prices or amounts) in simple consumer math scenarios.
Use simple multiplication to adjust quantities and total costs in a table row.
Use simple subtraction to find unknown values by comparing and subtracting rows in a table.
Solve two-part consumer math problems by finding two unknown values using the organized table method.
Check their solutions to ensure they make sense in the original problem.
Have you ever gone shopping and wondered about the secret prices of items? 🕵️♀️ What if you had two different shopping lists, and you needed to figure out the individual cost of each item?
In this lesson, you'll learn a super organized wa...
2
Key Concepts & Vocabulary
TermDefinitionExample
System of Equations (Grade 5 Version: Related Shopping Facts)Two or more related pieces of information or shopping scenarios that involve the same mystery items, helping you figure out their individual prices or quantities.Fact 1: 'You bought 2 apples and 1 banana for $3.' Fact 2: 'Your friend bought 2 apples and 3 bananas for $5.'
Augmented Matrix (Grade 5 Version: Organized Problem Table)A special table used to neatly arrange numbers from related shopping facts. It has columns for each mystery item and a column for the total cost, separated by a line, making it easier to solve.A table with columns like 'Apples', 'Bananas', and 'Total Cost', with rows for each shopping fact.
Unknowns (Grade 5 Version: Mystery Prices...
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Core Formulas
Multiply a Row in Your Table
$(Item_1 \text{ quantity}, Item_2 \text{ quantity} \mid \text{Total Cost}) \times N = (Item_1 \text{ quantity} \times N, Item_2 \text{ quantity} \times N \mid \text{Total Cost} \times N)$
This rule helps you change a shopping list to represent buying more (or less) of everything. If you know the cost of 1 apple and 2 bananas for $3, you can find the cost of 2 apples and 4 bananas by multiplying all numbers in that row by 2. This helps make one item's quantity match another row.
Subtract Rows in Your Table
$(A_1, B_1 \mid \text{Total}_1) - (A_2, B_2 \mid \text{Total}_2) = (A_1 - A_2, B_1 - B_2 \mid \text{Total}_1 - \text{Total}_2)$
When you have two shopping facts (two rows in your table) where some items are the same, you can subtract one ro...
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Challenging
Maria bought 2 game tickets and 3 ride tickets for $13. David bought 3 game tickets and 2 ride tickets for $12. What is the price of one game ticket and one ride ticket?
A.Game ticket: $2.00, Ride ticket: $3.00
B.Game ticket: $3.00, Ride ticket: $2.00
C.Game ticket: $2.50, Ride ticket: $2.50
D.Game ticket: $1.00, Ride ticket: $4.00
Challenging
The final step of solving a problem was subtracting to get (0 hats, 2 scarves | $18). This result came from subtracting (5, 3 | $57) - (5, 1 | $39). Which of the following could have been the two *original* shopping facts before any multiplication was done?
A.(5, 3 | $57) and (1, 1 | $13)
B.(1, 1 | $13) and (5, 3 | $57)
C.(2, 2 | $26) and (5, 1 | $39)
D.(10, 2 | $78) and (5, 3 | $57)
Challenging
Problem: '3 shirts and 4 pants cost $92. 1 shirt and 2 pants cost $36.' A student sets up the table as [3, 1 | $92] and [4, 2 | $36]. They solve and get the wrong answer. What was their mistake in the setup?
A.They swapped the total costs for the two rows.
B.They should have put pants in the first column and shirts in the second.
C.They added the numbers instead of writing them down.
D.In the first row, they used the quantity of pants (4) instead of shirts (3) for the first column, and in the second row, they mixed up the columns.
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