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Unit 3 · Standard 6.AT.2

Solve Problems with Unit Rates

Lesson 3-8 · Learn It — how the math works

Why we're learning this

You're the new supply manager for the arcade! You need to order tokens, prizes, and snacks from different suppliers. Each supplier offers a different package deal. Your job is to find the unit rate for each deal and figure out which supplier gives you the best value for every item you need to order. Fun Supply Co. sells 500 tokens for $60. Arcade Depot sells 350 tokens for $38.50. Which supplier gives the better value for tokens?

✱ Math Workbench

Learn It

How do I use unit rates to find the better buy?

A unit rate is the cost for just 1 item, like the price per token. When packages have different sizes, the unit rate lets you compare them fairly.

Picture itSee what the math looks like before you read about it

A supermarket shelf tag shows two deals side by side for the same brand of juice boxes: a 6-pack for $3.00 and a 10-pack for $4.50.
Where you see this in real lifeA supermarket shelf tag shows two deals side by side for the same brand of juice boxes: a 6-pack for $3.00 and a 10-pack for $4.50.

Watch me solve itI do — read one step at a time

The problem looks like this
Double number line: 500 tokens cost $60, so 1 token costs $0.12.Tokens1500Cost$0.12$60
  1. Fun Supply Co. sells 500 tokens for $60. I want the cost for 1 token.
  2. I divide the price by the tokens:$60 ÷ 500 = $0.12
  3. So this deal is $0.12 per token. That is the .
  4. Now I can compare it fairly to a deal with a different number of tokens.

Watch out — mistakes students make here

  • The unit rate is miles per gallon.
  • Divide 195 miles by 6 gallons to find the unit rate.
  • Find: 195 ÷ 6 = ? miles per gallon.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Arcade Depot sells 350 tokens for $38.50. What do we divide?
  2. We divide price by tokens: $38.50 ÷ 350 = ?$38.50 ÷ 350
  3. What is the cost per token, and is it lower than $0.12?
    Check this step
    ($0.11 — yes, the .)

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the table, find the for each supplier by dividing price by quantity.
  • Mark the option with the lower as the .

Solve: Find the for each deal and identify the .

OptionDealUnit Rate
Store A Batteries8 for $6.00
Store B Batteries12 for $8.40
Store A Candy15 for $6.75
Store B Candy20 for $8.00

Stuck? Open one hint at a time.

Hint 1

Every row is the same move: price ÷ quantity = cost of ONE battery or one piece of candy.

Hint 2

Find all four unit rates, then compare Store A vs Store B within each item (batteries vs batteries, candy vs candy).

Hint 3

Start with Store A batteries: $6.00 ÷ 8. Then $8.40 ÷ 12, $6.75 ÷ 15, and $8.00 ÷ 20.

Check my answer
✅ Answers:
  • Store A Batteries → Unit Rate: $0.75 each
  • Store B Batteries → Unit Rate: $0.70 each
  • Store A Candy → Unit Rate: $0.45 each
  • Store B Candy → Unit Rate: $0.40 each
Dividing each price by its quantity gives the cost of one item: $6.00 ÷ 8 = $0.75 and $8.40 ÷ 12 = $0.70 for batteries, $6.75 ÷ 15 = $0.45 and $8.00 ÷ 20 = $0.40 for candy. Store B wins both comparisons even though both of its deals carry the higher total price.

Turn & TalkSay it out loud with a partner

As supply manager you compare token deals like 500 for $60 and 350 for $38.50. You can't compare totals directly, so what does finding the cost '' let you do?

Try starting with:

  • I can't compare the totals because ___.No puedo comparar los totales porque ___.
  • Finding the cost ___ lets me compare fairly.Hallar el costo ___ me deja comparar de forma justa.
Use these wordsunit rateper unitcomparisonrate