Question

7.

About a third of the blueberry crop was ruined by a sudden frost. A
sixth of the undamaged blueberries spoiled on the way to market. How
much of the original blueberry crop made it to the market unspoiled
and undamaged?
A.1/9
B.1/3
C. 5/9
D.7/9

Answer 1

C. 5/9

Explanation:

Given: 1/3 BC (blueberry crop) ruined, 1/6 BC spoiled

explanation a:

let us suppose that the blueberry crop equals to 45 (tho using 100 is a better option)

1/3 of the crop was ruined by the frost; therefore, we have the equation:

45/3 = 15

now we will minus 45 out of 15 to find the value preceding the frost.

45-15 = 30

1/6 of the surviving blueberries was spoiled on the way; therefore, we have the equation:

30/6 = 5

now we will minus 5 out of 30 to find the value preceding the spoil.

30 - 5 = 25

lastly, we will plug the final value (25) as a fraction of 45

25/45 = 5/9

explanation b (using 100):

let us suppose that the blueberry crop equals to 100.

1/3 of the crop was ruined by the frost; therefore, we have the equation:

100/3 = 33.3

now we will minus 33.3 out of 100 to find the value preceding the frost.

100- 33.3 = 66.6

1/6 of the surviving blueberries was spoiled on the way; therefore, we have the equation:

66.6/6= 11.1

now we will minus 11. 1 out of 66.6 to find the value preceding the spoil.

66.6 - 11.11 = 55.56

lastly, we will plug the final value (55.5) as a fraction of 100

55.56/100 = 5/9

Answer 2

Let's assume that the original blueberry crop was 100 units. Then, one-third of the blueberry crop, or 100/3 = 33.33 units, was ruined by the frost. This means that the remaining undamaged blueberries are 100 - 33.33 = 66.67 units.

Next, one-sixth of the undamaged blueberries spoiled on the way to the market. One-sixth of 66.67 is (1/6)*66.67 = 11.11 units. Therefore, the amount of blueberries that made it to the market unspoiled and undamaged is 66.67 - 11.11 = 55.56 units.

Now, we can find the fraction of the original blueberry crop that made it to the market unspoiled and undamaged by dividing the amount of blueberries that made it to the market by the original amount of blueberries:

55.56 / 100 = 5/9

Therefore, the answer is C. 5/9 of the original blueberry crop made it to the market unspoiled and undamaged.