Analysis of Kiran's Lentil Purchase

Kiran says, "I bought 2.5 pounds of red and yellow lentils. Both were $1.80 per pound. I spent a total of $4.05." (Lesson 2-17)

a. Write a system of equations to describe the relationships between the quantities in Kiran's statement. Be sure to specify what each variable represents.

b. Elena says, "That can't be right." Explain how Elena can tell that something is wrong with Kiran's statement.

Question:

How can Elena identify that there is an error in Kiran's statement regarding the purchase of lentils?

Final answer:

A student is asked to write a system of equations based on Kiran's purchase of lentils. There's a discrepancy in Kiran's statement about how much was spent on the lentils. After calculating, we identify that Kiran's total expenditure does not match the expected cost at the stated price per pound.

Explanation:

Kiran's statement involves buying a total of 2.5 pounds of lentils at a rate of $1.80 per pound. The system of equations to represent this scenario involves only one equation because we are dealing with just one type of item (lentils) bought at a single price.

Let x be the total pounds of lentils Kiran bought. According to Kiran, x should be 2.5, and the total cost should be $4.05. The equation derived from Kiran's statement would be:

1.80x = 4.05

However, Elena is correct to suspect that there is an error in Kiran's statement. To verify this, we simply calculate the total cost if Kiran bought 2.5 pounds at $1.80 per pound, which equals $4.50 (2.5 pounds × $1.80 per pound). Since Kiran said they spent $4.05, this is less than what they would have spent if the price per pound was $1.80. Thus, the amount spent does not match the given price per pound and quantity.