Lesson 3.8Solve Problems with Unit Rates
Start hereWords, worked example, and sentence starters
Learning target I can solve real-world problems by using unit rates to compare options.
Why This Matters 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?
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Unit RateSpanish: Tasa unitaria | A rate for just 1 of something, like cost for 1 item. | $2.50 per pound means $2.50 for every 1 pound |
| Better BuySpanish: Mejor compra | The choice that costs less for each item. | $0.10 each vs $0.15 each — the $0.10 option is the better buy |
| ComparisonSpanish: Comparación | Looking at two or more amounts to see how they are related. | $3 per game < $4 per game |
| Per UnitSpanish: Por unidad | For each single item. | $0.50 per token means each token costs $0.50 |
| RateSpanish: Tasa | A ratio comparing two amounts with different units, like miles per hour. | 120 miles in 3 hours is a rate (miles and hours are different units) |
| ProportionSpanish: Proporción | A math sentence saying two ratios are equal. It helps find a missing number. | 5/3 = x/12 → x = 20 |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Fun Supply Co. sells 500 tokens for $60. I want the cost for 1 token.
- I divide the price by the tokens: $60 ÷ 500 = $0.12.
- So this deal is $0.12 per token. That is the unit rate.
- Now I can compare it fairly to a deal with a different number of tokens.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Arcade Depot sells 350 tokens for $38.50. What do we divide?
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- I find the better buy by comparing the for each option. The option with the unit rate is the better buy because .
Word bank Unit RateBetter BuyComparisonPer UnitRateProportionunit ratelowerdividecostpercompare
Watch out!A common mistake
A common mistake in Solve Problems with Unit Rates is comparing the total prices instead of the cost per item
Lesson 3.8Solve Problems with Unit Rates
Level 0Most support · every hint printed
Learning target I can solve real-world problems by using unit rates to compare options.
Why This Matters 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?
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Fun Supply Co. sells 500 tokens for $60. I want the cost for 1 token.
- I divide the price by the tokens: $60 ÷ 500 = $0.12.
- So this deal is $0.12 per token. That is the unit rate.
- Now I can compare it fairly to a deal with a different number of tokens.
-
1Circle the letter of the best answer. Show how you know.
Which is the better buy: 6 bouncy balls for $4.50 or 10 bouncy balls for $8.00?
- A10 for $8.00 — $0.80 each
- BThey cost the same per ball
- CNot enough information
- D6 for $4.50 — $0.75 each
Steps to try- You can't compare $4.50 and $8.00 straight across — the packs hold different numbers of balls.
- Find each pack's price for ONE ball (cost ÷ number of balls), then compare the two unit prices.
- Start with the first deal: $4.50 ÷ 6. Then compute $8.00 ÷ 10 and see which per-ball price is lower.
Show your work -
2Circle the letter of the best answer. Show how you know.
A faucet drips 15 ounces of water in 5 minutes. What is the unit rate?
- A0.33 ounces per minute
- B3 ounces per minute
- C5 ounces per minute
- D15 ounces per minute
Steps to try- The unit rate here is ounces per ONE minute — 15 ounces spread across 5 minutes.
- Divide the ounces by the minutes so the time becomes 1 minute.
- Set up 15 ÷ 5 ounces per minute.
per 1 - 1LabelWrite what each column is.
- 2Find per 1Divide to get one.
- 3ScaleMultiply up to what is asked.
- 4CheckDoes the size make sense?
-
3Circle the letter of the best answer. Show how you know.
A printer prints 42 pages in 6 minutes. How many pages does it print in 15 minutes at the same rate?
- A70 pages
- B90 pages
- C105 pages
- D120 pages
Steps to try- This takes two steps: first find pages per ONE minute, then scale up to 15 minutes.
- Divide to get the unit rate, then multiply that rate by the new time.
- Step 1: 42 ÷ 6 = 7 pages each minute. Step 2: multiply that rate by 15 minutes.
Show your work -
4Circle the letter of the best answer. Show how you know.
Store A sells 5 notebooks for $8. Store B sells 3 notebooks for $5.25. Which has the lower price per notebook?
- AStore B ($1.75 each)
- BStore A ($1.60 each)
- CSame price
- DCannot determine
Steps to try- Each store sells a different number of notebooks, so compare the price of ONE notebook at each store.
- Divide cost by quantity for each store, then pick the smaller per-notebook price.
- Store A: $8 ÷ 5 notebooks. Then compute Store B: $5.25 ÷ 3, and compare the two prices.
Show your work
Explain your thinkingHow do you use unit rates to determine the better buy?
Sentence starter I find the better buy by comparing the ___ for each option. The option with the ___ unit rate is the better buy because ___.