Carrots cost 75 cents per kilogram and potatoes cost 70 cents per kilogram. a shopper bought 9 kg of the vegetables for $6.60. how many kilograms of each did the shopper buy?

Let us assume that the weight of carrots is "X" kilogram

Since the total weight is 9 kilograms, the weight of potatoes should be "9-X" kilograms.

The cost of "X" kilograms of carrot at $0.75/kilogram is calculated as = 0.75*X = 0.75X

The cost of "9-X" kilograms of potatoes at $0.70/kilogram is calculated as 0.70 * (9-X)

We know that the total cost is $6.60

We now frame the equation as:

0.75X + (9-X) * 0.70 = 6.60

0.75X + 6.30 - 0.70X = 6.60

0.05X = 0.30

X = 0.30/0.05 = 30/5 = 6

Therefore weight of carrots = 6 Kilograms and

Weight of potatoes = 9-6 = 3 Kilograms

Amount of Carrot bought at $0.75 per kilogram = x

Amount of potatoes bought at $0.70 per kilogram = y

Since, a shopper bought 9 kg of the vegetables.

Therefore, x + y = 9 (equation 1)

A shopper bought 9 kg of vegetables at $6.60.

Therefore, 0.75x+0.70y=6.60

Multiplying the above equation by 100.

75x+70y=660 (equation 2)

Multiplying equation 1 by '-75' and adding it to the equation 2, we get

-75x-75y+75x+70y = 660-675

-5y = - 15

y = 3

x + y = 9

x + 3 = 9

x = 9 - 3 = 6

Therefore, the shopper bought 6kg of carrots and 3 kg of potatoes.