Unit Rate Comparisons - SSAT Upper Level Quantitative

1. What is the unit price for $12 for $3$ notebooks?

   $4 per notebook. Divide the total cost by the number of notebooks to determine the price per individual unit.

2. Which is a better price per minute: $24 for $8$ min or $15 for $5$ min?

   Neither; both are $3 per minute. Compare rates by dividing cost by minutes; identical prices per minute mean no difference.

3. Which is faster: $240$ miles in $4$ hours or $180$ miles in $3$ hours?

   Neither; both are $60$ miles per hour. Compare speeds by dividing distance by time for each; equal rates indicate no difference in speed.

4. What is the unit rate in dollars per hour for $96 for $8$ hours of work?

   $12 per hour. Find hourly wage by dividing total earnings by hours worked to express pay per unit time.

5. What is the unit rate in dollars per pound for $9 for $4$ pounds?

   $2.25 per pound. Calculate the rate by dividing cost by pounds to determine price per unit weight.

6. What is a unit rate?

   A rate per $1$ unit of the second quantity (for example, dollars per $1$ item). A unit rate simplifies a ratio by expressing the first quantity relative to one unit of the second, enabling easy comparisons across different scales.

7. What is the unit rate in dollars per minute for $18 for $6$ minutes of parking?

   $3 per minute. Compute the rate by dividing cost by minutes to find expense per unit time.

8. Which car is more fuel-efficient: $300$ miles on $10$ gal or $280$ miles on $8$ gal?

   $280$ miles on $8$ gal. Compare fuel efficiency by dividing miles by gallons; higher miles per gallon indicates better performance.

9. What is the unit rate in words per minute for $900$ words in $6$ minutes?

   $150$ words per minute. Determine typing speed by dividing words by minutes to find the rate per unit time.

10. What is the unit rate in miles per gallon for $360$ miles using $12$ gallons?

    $30$ miles per gallon. Calculate efficiency by dividing miles by gallons to determine distance per unit fuel.

11. Which is the better value: $18$ items for $6 or $20$ items for $8?

    $18$ items for $6. Evaluate value by dividing items by cost; higher items per dollar provide better value.

12. What is the unit rate in items per dollar for $15$ items costing $5?

    $3$ items per dollar. Calculate the rate by dividing items by cost to express quantity obtained per unit currency.

13. What is the pace in minutes per mile for $30$ minutes over $5$ miles?

    $6$ minutes per mile. Determine pace by dividing total time by distance to express minutes required per mile.

14. What is the unit rate in pages per minute for $45$ pages in $9$ minutes?

    $5$ pages per minute. Calculate the rate by dividing pages by minutes to express productivity per unit time.

15. What is the speed in miles per hour for $150$ miles in $3$ hours?

    $50$ miles per hour. Calculate speed by dividing total distance by time to find miles traveled per hour.

16. Which is a better deal per item: $14 for $7$ items or $9 for $4$ items?

    $14 for $7$ items. Assess value by dividing cost by items; the lower price per item represents the better deal.

17. What is the unit rate in dollars per day for $45 for $9$ days?

    $5 per day. Compute daily rate by dividing total cost by days to express expense per unit time.

18. What is the unit rate in gallons per minute for $12$ gallons in $3$ minutes?

    $4$ gallons per minute. Compute the rate by dividing gallons by minutes to express flow per unit time.

19. Which is cheaper per ounce: $3.60 for $12$ oz or $4.50 for $18$ oz?

    $4.50 for $18$ oz. Evaluate cost-effectiveness by dividing price by ounces; the lower unit cost per ounce is cheaper.

20. Which earns a higher hourly rate: $150 for $12$ hours or $130 for $10$ hours?

    $130 for $10$ hours. Compare rates by dividing earnings by hours; the higher pay per hour is more lucrative.

21. What is the unit rate in dollars per item for $27 for $9$ items?

    $3 per item. Determine cost per item by dividing total price by number of items.

22. Which is larger: $\frac{7}{2}$ dollars per item or $\frac{10}{3}$ dollars per item?

    $\frac{7}{2}$ dollars per item. Compare the fractions directly; $\frac{7}{2} = 3.5$ exceeds $\frac{10}{3} \approx 3.333$, making it larger.

23. What is the unit rate in dollars per pound for $7.50 for $3$ pounds?

    $2.50 per pound. Find the rate by dividing total cost by pounds to determine price per unit weight.

24. Which is the better buy: $18 for $6$ bottles or $20 for $8$ bottles?

    $20 for $8$ bottles. Compare unit prices by dividing cost by quantity; the option with the lower price per bottle offers better value.

25. What is the unit rate in cups per person for $12$ cups shared by $8$ people?

    $1.5$ cups per person. Find the share by dividing total cups by people to express amount per individual.

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