Mathematics Grade 5 15 min

Classify a system of equations

Classify a system of equations

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1

Introduction & Learning Objectives

Learning Objectives Identify two different ways to calculate a total cost. Calculate the total cost for different options given a quantity. Compare the total costs of two different options to determine which is cheaper or more expensive. Determine if two different cost options can ever have the same total cost for a specific quantity. Use simple tables or calculations to organize and compare cost information. Make informed decisions about which consumer option is best based on cost comparisons. Have you ever wondered which store has the best deal, or which club membership is cheaper? 💰 Today, we'll learn how to compare different ways to pay for things! In this lesson, you will learn how to look at two different ways to calculate a total cost, which we'll call &#0...
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Key Concepts & Vocabulary

TermDefinitionExample Cost Option/PlanA specific way that a total price is calculated, often including a fixed fee and a cost per item or per unit.Plan A: $5 fee plus $2 per game. Plan B: $3 per game with no fee. Fixed CostA one-time payment or fee that does not change, no matter how many items you buy or how much you use a service.A $10 membership fee for a club, or a $20 rental fee for a party room. Variable CostA cost that changes based on the quantity of items bought or the amount of service used. It's usually given as a 'cost per item' or 'cost per minute'.Paying $3 for each apple, or $0.10 for each minute of phone use. Total CostThe final amount of money you have to pay, which includes all fixed costs and variable costs.If you pay a $5 fee and $2 for 3 games...
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Core Formulas

Total Cost Calculation Rule Total Cost = Fixed Cost + (Cost per Item $\times$ Number of Items) Use this rule to find the total amount you will pay for any option. Remember that if there is no fixed cost, you can think of it as $0. Comparing Options Rule Calculate Total Cost for Option 1. Calculate Total Cost for Option 2. Compare the two total costs using $<$, $>$, or $=$. To decide which option is better, always calculate the full total cost for each choice first, then look at the numbers to see which is lower (for saving money) or higher.

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Sample Practice Questions

Challenging
You have a $25 gift card for a frozen yogurt shop. Option 1: A $4 cup fee, plus $1.50 per ounce. Option 2: A $2 cup fee, plus $2.00 per ounce. Which option allows you to buy the most yogurt without going over your $25 limit?
A.Option 1 allows you to buy more yogurt.
B.Option 2 allows you to buy more yogurt.
C.Both options allow you to buy the same amount.
D.Neither option allows you to buy any yogurt.
Challenging
A gym offers two plans. Plan A: $20 fee, $5 per visit. Plan B: $10 fee, $6 per visit. They cost the same at 10 visits. If Plan A lowered its fee to $15, at how many visits would they now cost the same?
A.10 visits
B.5 visits
C.15 visits
D.They will never cost the same.
Challenging
Two internet plans are offered. Plan A: $30/month plus $2 per hour of premium access. Plan B: $20/month plus $2.50 per hour of premium access. At how many hours of premium access do the plans cost the same, and which plan is cheaper if you use MORE than that amount of hours?
A.10 hours; Plan B is cheaper after that.
B.10 hours; Plan A is cheaper after that.
C.20 hours; Plan A is cheaper after that.
D.20 hours; Plan B is cheaper after that.

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