Question

1. theo’s mom bought an eight - pack of juice boxes at the store for $4. find the unit rate for the juice boxes. (example 4)
2. joshua’s cousin pledged $12 for a charity walk. if joshua walked 3 miles, how much did his cousin pay per mile? (example 4)
3. justify conclusions the lovin’lemon company sells a 4 - gallon jug of lemonade for $24. the sweet and sour company sells an eight - pack of 1 - quart bottles of lemonade for $16.00. which company has a higher unit price? explain your answer.

9 the shanghai maglev train is one of the fastest trains in the world, traveling about 2,144 miles in 8 hours.
a. how many miles does it travel in one hour?
b. the distance between columbus, ohio, and new york city is about 560 miles. how many hours would it take the train to travel between the cities?

Explanation:

Question 6

Step1: Recall unit rate formula

Unit rate is total cost divided by number of units, so \(\text{Unit Rate}=\frac{\text{Total Cost}}{\text{Number of Units}}\).

Step2: Substitute values

Total cost is \$4, number of units (juice boxes) is 8. So \(\text{Unit Rate}=\frac{4}{8}\).

Step3: Simplify the fraction

\(\frac{4}{8} = 0.5\) dollars per juice box.

Step1: Recall unit rate formula

Unit rate (per mile) is total pledged amount divided by miles walked, so \(\text{Unit Rate}=\frac{\text{Total Pledged}}{\text{Miles Walked}}\).

Step2: Substitute values

Total pledged is \$12, miles walked is 3. So \(\text{Unit Rate}=\frac{12}{3}\).

Step3: Simplify the division

\(\frac{12}{3}=4\) dollars per mile.

Step1: Convert units for Lovin' Lemon

1 gallon = 4 quarts, so 4 - gallon jug is \(4\times4 = 16\) quarts. Cost is \$24. Unit price (per quart) is \(\frac{24}{16}\).

Step2: Calculate unit price for Lovin' Lemon

\(\frac{24}{16}=1.5\) dollars per quart.

Step3: Calculate unit price for Sweet and Sour

Eight - pack of 1 - quart bottles, cost \$16. Unit price is \(\frac{16}{8}=2\) dollars per quart.

Step4: Compare unit prices

Since \(2>1.5\), Sweet and Sour Company has higher unit price.

Answer:

The unit rate is \$0.5 per juice box.

Question 7