Question

Last summer we went camping in Yosemite, and the first night we did a bad thing: we left out food on the ground. A bear came along and ripped up one-third of our total number of dried meals. The next day we ate four of the remaining meals and tied the food up in a tree. It didn’t seem to help because one-third of the meals we had left were ripped open by another bear. During our third day, we ate four more meals and that night, despite everything we did, one-half of our remaining dried meals were ripped apart. We gave up, ate the four remaining dried meals, and headed home. Can you tell how many dried meals we started with?

Answer 1

Answer: We started with 36 dried meals

Step-by-step explanation: Let x be the number of dried meals we started with. After the first night, we had x - x/3 = 2x/3 meals left. After the second day, we had 2x/3 - 4 meals left. After the second night, we had (2x/3 - 4) - (2x/3 - 4)/3 = 4x/9 - 8/3 meals left. After the third day, we had (4x/9 - 8/3) - 4 meals left. After the third night, we had ((4x/9 - 8/3) - 4)/2 meals left. This was equal to 4, so we can set up an equation and solve for x:

((4x/9 - 8/3) - 4)/2 = 4

Multiplying both sides by 2, we get:

(4x/9 - 8/3) - 4 = 8

Adding 4 to both sides, we get:

4x/9 - 8/3 = 12

Multiplying both sides by 9, we get:

4x - 24 = 108

Adding 24 to both sides, we get:

4x = 132

Dividing both sides by 4, we get:

x = 33

However, if x = 33, then the number of dried meals we had left after the third night would be ((4*33/9 - 8/3) - 4)/2 = 4.666… This is not a whole number, so it means that we either had more or less than 4 meals left. Since we ate the four remaining meals and headed home, we know that we had exactly 4 meals left. Therefore, x cannot be 33. The closest integer to 33 that satisfies the equation is 36.

Hope this helps, and have a great day! =)

Answer 2

33 meals

Explanation:

You want to know the number of meals you started with if 4 were left after half those at the end of the third day were destroyed, 4 were eaten on the third day after 1/3 those at the end of the second day were destroyed, 4 were eaten on the second day after 1/3 of the starting number were destroyed.

Scenario

Assume we started with x meals. The sequence of events seems to be ...

1/3 were destroyed overnight, so 2/3x remained

4 were eaten next day, so (2/3x -4) remained

1/3 were destroyed overnight, so 2/3(2/3x -4) remained

4 were eaten on the third day, so 2/3(2/3x -4) -4 remained

1/2 were destroyed, so 1/2(2/3(2/3x -4) -4) remained

The number remaining was 4.

Solution

Undoing the layers of the expression, we have ...

1/2(2/3(2/3x -4) -4) = 4

2/3(2/3x -4) -4 = 8 . . . . . . . multiply by 2

2/3(2/3x -4) = 12 . . . . . . . . . add 4

2/3x -4 = 18 . . . . . . . . . . . . . multiply by 3/2

2/3x = 22 . . . . . . . . . . . . . . . add 4

x = 33 . . . . . . . . . . . . . . . . . . multiply by 3/2

You started with 33 meals.

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