Final answer:
The price per song is $0.75, and the correct equation relating price to the number of songs is C = 0.75n. Unit rates for given quantities are calculated and equations are formed. To determine better buys when comparing packs to single items, calculate and compare the unit prices.
Step-by-step explanation:
The price per song can be calculated by dividing the total cost by the number of songs Keeley bought. So we have $26.25 divided by 35 songs to get a price per song, which is $26.25 ÷ 35 = $0.75 per song.
After completing the table, we consider Lucius's equation n = 0.75C and Javier's equation C = 0.75n. The correct equation is Javier's because it represents the total cost C as a product of the number of songs n and the price per song. Thus, C = 0.75n is valid.
Finding Unit Rates and Equations
For 3 dozen apples costing $4.50, the unit rate is $1.50 per dozen. The equation is C = 1.50d, where C is the cost and d is the dozen apples.
For 30 bottles of water costing $4.80, the unit rate is $0.16 per bottle. The equation is C = 0.16b, where C is the cost and b is the number of bottles.
For 24 ounces of mozzarella cheese costing $2.88, the unit rate is $0.12 per ounce. The equation is C = 0.12o, where C is the cost and o is the number of ounces.
Comparing Costs for Bulk vs. Single Items
To determine which items are better buys:
Divide $3.99 by 8 to get the price per glue stick in the pack, and compare it with $0.54 for a single glue stick.
Divide $2.50 by 12 to get the price per roll of tape in the pack, and compare it with $0.19 for a single roll of tape.
Divide $4.88 by 100 to get the price per pencil in the pack, and compare it with $0.05 for a single pencil.
Divide $0.89 by 50 to get the price per paper clip in the pack, and compare it with the cost of $0.45 divided by 25 for a single paper clip in the smaller pack.
By comparing these unit prices, you can determine which option provides more value and is therefore the better buy.