Mathematics
Grade 5
15 min
Solve a system of equations using elimination
Solve a system of equations using elimination
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1
Introduction & Learning Objectives
Learning Objectives
Identify two related consumer math scenarios.
Recognize a common item or quantity between two scenarios.
Use subtraction to find the difference in total cost or quantity when a common item is present.
Calculate the cost or quantity of a single unknown item after eliminating a common item.
Substitute a known value back into an original scenario to find another unknown.
Solve simple consumer math problems using the elimination strategy.
Ever wonder how stores figure out the price of just one apple when you buy a whole bag, or how many cookies one cup of sugar makes? 🍎💰 Let's become math detectives!
In this lesson, you'll learn a clever trick called 'elimination' to solve shopping and recipe puzzles. This strategy helps us find the pri...
2
Key Concepts & Vocabulary
TermDefinitionExample
System of Equations (Simplified)Two or more math puzzles or shopping lists that are related and need to be solved together to find unknown values.Scenario 1: '2 apples + 3 bananas = $5' and Scenario 2: '2 apples + 5 bananas = $7' form a system.
EliminationA strategy to remove (or 'eliminate') one unknown item from our math puzzles by comparing or subtracting the puzzles, making it easier to solve for another item.If both shopping lists have '2 apples', we can 'eliminate' the apples to focus on the bananas.
UnknownA quantity or price that we don't know yet and want to find in our math puzzle.The price of one banana or one apple is an unknown until we solve the puzzle.
Common ItemAn item that appears in the exact s...
3
Core Formulas
Rule for Finding the Difference
$\text{Total Difference in Cost} = \text{Larger Total Cost} - \text{Smaller Total Cost}$
Use this rule to find how much more was spent (or how many more items were made) when one scenario has more of a certain item than another, after identifying and 'eliminating' the common item.
Rule for Finding the Value of One Extra Item
$\text{Cost/Quantity of 1 Extra Item} = \frac{\text{Total Difference in Cost/Quantity}}{\text{Number of Extra Items}}$
Once you know the total difference in cost or quantity and how many extra items caused that difference, divide to find the price or quantity made by just one of those items.
Rule for Substitution
$\text{Known Item Value} \rightarrow \text{Original Scenario}$
After finding the value of one...
4 more steps in this tutorial
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Challenging
In a system of equations where 'Scenario B' has a higher total cost than 'Scenario A', and both have 'Item X' in common, but 'Scenario B' has more of 'Item Y', what does the difference in total cost represent?
A.The total cost of all the items in Scenario B.
B.The cost of only the extra units of 'Item Y'.
C.The cost of one unit of 'Item X'.
D.The average cost of 'Item X' and 'Item Y'.
Challenging
A student correctly determines that the difference between two batches of lemonade is 3 extra lemons and 6 extra cups of lemonade sold. They use a formula from the tutorial to find that 1 extra lemon makes 2 cups of lemonade. Which formula did they use?
A.Quantity of 1 Extra Item = Total Difference in Quantity / Number of Extra Items
B.Total Difference in Cost = Larger Total Cost - Smaller Total Cost
C.Substitution: Original Amount + Extra Amount = Total
D.Number of Extra Items = Total Difference / Cost of 1 Item
Challenging
You know that 1 scarf costs $8. Your first purchase is: 3 hats and 1 scarf cost $23. If you want to create a second purchase scenario that allows you to use elimination to find the price of a hat, which of these would work?
A.3 hats and 2 scarves cost $30
B.2 hats and 1 scarf cost $18
C.4 hats and 1 scarf cost $28
D.3 hats and 3 scarves cost $39
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