7th Grade Math Test 2

 

 Based on the West Virginia College- and Career-Readiness Standards for 7th grade, a core focus is on Ratios and Proportional Relationships. A typical question found on the West Virginia General Summative Assessment (WVGSA) involves calculating unit rates to determine the "better buy" or comparing different speeds.

 

Opens in a new window wvde.us

The Math Problem

Question: A local grocery store in Lewisburg sells two brands of apple juice. Brand A costs $4.50 for a 64-ounce bottle. Brand B costs $2.40 for a 32-ounce bottle. Which brand is the better buy based on the price per ounce?

---

Step-by-Step Solution

To solve this, we must find the unit rate for each brand. The unit rate tells us the cost of exactly one ounce of juice, allowing for a fair comparison.

Step 1: Calculate the Unit Rate for Brand A

The formula for unit price is: Total Cost ÷ Total Quantity

• Cost: $4.50

• Quantity: 64 ounces

• Calculation: $4.50 / 64 = 0.0703125$

When dealing with money, we round to the nearest cent. However, for precise comparisons, it is helpful to look at the third decimal place.

• Brand A Price per Ounce: approximately $0.070 (or 7 cents).

Step 2: Calculate the Unit Rate for Brand B

• Cost: $2.40

• Quantity: 32 ounces

• Calculation: $2.40 / 32 = 0.075$

• Brand B Price per Ounce: exactly $0.075 (or 7.5 cents).

Step 3: Compare the Results

Now, we compare the two unit prices:

• Brand A: $0.070 per ounce

• Brand B: $0.075 per ounce

Step 4: Formulate the Final Answer

Since $0.070 is less than $0.075, Brand A is the better buy. Even though the bottle is more expensive upfront, you are paying half a cent less for every ounce of juice you consume.

West Virginia Standard Alignment:

This problem addresses standard M.7.1, which requires students to analyze proportional relationships and use them to solve real-world and mathematical problems, specifically computing unit rates associated with ratios of fractions or decimals.