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

Answer 1

Answer:

Carrots cost $ 1.75 a pound which is more than potatoes cost.

Step-by-step explanation:

Let,

Carrots cost $ x per pound and potatoes cost $ y per pound.

Buying 2 pounds of carrots  and 3 pounds of potatoes will cost her

$ $(2\times x + 3\times y)$

and

Buying 4 pounds of carrots and 4 pounds of potatoes will cost her

$ $(4\times x + 4\times y)$

According to the question,

$(2\times x + 3\times y) = 8$-----(1)

$(4\times x + 4\times y) = 13$-----(2)

multiplying (1) by 2 we get,

$(4\times x + 6\times y) = 16$-----(3)

Deducting (2) from (3) we get,

$2\times y = 3$

⇒ $y = \frac{3}{2} = 1.5$------------------(4)

Putting value of y in (1) we get,

$(2\times x = 8 - 3\times 1.5) = 3.5$

⇒  $x =\frac{3.5}{2} = 1.75$ ------------(5)