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 will cost her a total of $13. How much does a pound of carrots cost?

Potato price = $1.5 / pound; Carrot price = $1.75 / pound

Step-by-step explanation:

Let price of carrot per pound = c

Let price of potatoes per pound = p

Given:

2c + 3p = 8 (eqtn A)

4c + 4p = 13 (eqtn B)

Multiplying eqtn A by 2;

4c + 6p = 16

4c = 16 - 6p (eqtn Y)

By eqtn B;

4c = 13 - 4p (eqtn Z)

By eqtn Y & Z;

16 - 6p = 13 - 4p

16 - 13 = - 4p + 6p

3 = 2p

p = 3 / 2

p = 1.5 [Potato price]

Putting p value in eqtn A

2c + 3 (1.5) = 8

2c + 4.5 = 8

2c = 8 - 4.5

2c = 3.5

c = 3.5 / 2

c = 1.75 [Carrot Price]