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Comparing and Scaling Rates: Investigation 2.3 Homework 1. Keeley buys songs from a music website. She buys 35 songs for $26.25. What is the price per song? a. Complete the table. b. Lucius and Javier discuss how to write an equation relating price and number of songs. Lucius writes the equation n = 0.75C. Javier writes the equation C = 0.75n. Do you agree with Lucius or with Javier? Use the information from parts (a) to explain. 2. For each situation, find a unit rate and write an equation relating the two quantities. a. 3 dozen apples for $4.50 b. 30 bottles of water for $4.80 c. 24 ounces of mozzarella cheese for $2.88 Number of Songs, n 35 50 1 70 Cost, C $26.25 $3 $15

0.75

37.50

cost

dozen

= 4.50/3 = $1.50 / dozen

cost/bottles

2 3. Which of these items is the better buy? a. an 8-pack of glue sticks for $3.99 or 1 glue stick for $.54 b. a 12-pack of tape for $2.50 or 1 roll of tape for $.19 c. a 100-pack of pencils for $4.88 or 1 pencil for $.05 d. a 50-pack of paper clips for $.89 or a 25-pack of paper clips for $.45.

User Schneems
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2 Answers

7 votes
7 votes

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.

User Vibert
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23 votes
23 votes

Answer:

Use the information from parts a

Step-by-step explanation:

User ThaDon
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