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

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

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* x + 3* y)`

and

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

$
`(4* x + 4* y)`

According to the question,

`(2* x + 3* y) = 8`-----(1)

`(4* x + 4* y) = 13`-----(2)

multiplying (1) by 2 we get,

`(4* x + 6* y) = 16`-----(3)

Deducting (2) from (3) we get,

`2* y = 3`

⇒
`y = (3)/(2) = 1.5`------------------(4)

Putting value of y in (1) we get,

`(2* x = 8 - 3* 1.5) = 3.5`

⇒
`x =(3.5)/(2) = 1.75` ------------(5)