Solve a system of equations using elimination word problems

Learning Objectives Identify two unknown quantities in consumer math word problems. Understand how two different shopping scenarios provide clues about unknown prices. Compare two related scenarios to find the difference in quantities and total cost. Use the difference between scenarios to calculate the unit price of one unknown item. Apply the value of one unknown item to find the value of the second unknown item. Solve word problems involving two unknown quantities in consumer math contexts. Ever wonder how stores figure out the price of each item when they sell things in bundles or different combinations? 🛍️💰 In this lesson, you'll learn a clever way to solve word problems where you need to find the price of two different items by comparing two shopping trips or si...

TermDefinitionExample Unknown QuantityA value or amount that we don't know yet and need to figure out, like the price of one apple or the number of pencils.In a problem about apples and bananas, the 'price of one apple' and the 'price of one banana' are unknown quantities. ScenarioA specific situation or event described in a word problem, usually involving a set of items and a total cost.One scenario might be '3 apples and 2 bananas cost $5.50'. Comparing ScenariosLooking at two different situations side-by-side to see what is the same and what is different between them.Comparing '3 apples and 2 bananas cost $5.50' with '3 apples and 4 bananas cost $8.50'. Finding the DifferenceSubtracting one scenario's quantities and total cost...

Total Cost Calculation `\text{Total Cost} = (\text{Quantity}_1 \times \text{Price}_1) + (\text{Quantity}_2 \times \text{Price}_2)` This rule shows how the total money spent in a shopping trip is found by adding up the cost of each type of item. You multiply the number of each item by its price, then add those amounts together. Finding the Difference in Cost `\text{Difference in Cost} = \text{Total Cost of Scenario A} - \text{Total Cost of Scenario B}` When you compare two scenarios, this rule helps you find how much more money was spent in one situation compared to the other. This difference in cost will match the difference in the items bought. Finding the Difference in Quantity `\text{Difference in Quantity} = \text{Quantity of Item in Scenario A} - \text{Quantity of...