Hannah is at the supermarket to buy carrots and potatoes. If she buys 2 pounds o

Question

Hannah is at the supermarket to buy carrots and potatoes. If she buys 2 pounds of carrots and 3 pounds of potatoes, it will cost her a total of $8, and if she buys 4 pounds of carrots and 4 pounds of potatoes, it Hill cost her a total of $13. Which of these statements is correct? Carrots cost $1.50 a pound, which is less than potatoes cost. Carrots cost $1.50 a pound, which is more than potatoes cost. Carrots cost $1.75 a pound, which is less than potatoes cost. Carrots cost $ 1.75 a pound, which is more than potatoes cost.

Explanation / Answer

Let the cost per lb of carrots and potatoes be x and y respectively.Then 2x + 3y=8...(1) and 4x +4y = 13 or, 2x+2y= 6.50...(2)

On subtracting the2nd equation from the 1st equation, we get 2x+3y - 2x -2y = 8 -6.50 or, y = 1.50 . Now, on substituting y = 1.50 in the 2nd equation, we get 2x +3.00 = 6.50 or, 2x = 6.50 - 3.00 = 3.50 so that x = 1/2(3.50) = 1.75.

Since 1.75 > 1.50, the last statement, i.e. option D is correct.

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