# Find the amount of sand in each bag

• MHB
• anemone
In summary, in the beginning, Bags $A,\,B$ and $C$ contained 360 g of sand in total. Then, $\dfrac{1}{6}$ of sand in Bag $A$ was poured into Bag $B$, followed by $\dfrac{1}{3}$ of sand in Bag $B$ being poured into Bag $C$, and finally $\dfrac{1}{5}$ of sand in Bag $C$ being poured into Bag $A$. In the end, there was an equal amount of 120 g of sand in each bag. By working backwards, we can determine that the original amounts of sand in each bag were 90 g in Bag $A$, 120 g in Bag $anemone Gold Member MHB POTW Director Bags$A,\,B$and$C$contained 360 g of sand in total. At first,$\dfrac{1}{6}$of sand in Bag$A$was poured into Bag$B$. Then,$\dfrac{1}{3}$of sand in Bag$B$is poured into Bag$C$. Lastly,$\dfrac{1}{5}$of sand in Bag$C$is poured into Bag$A\$. In the end, there was equal amount of sand in each bag.

Find the amount of sand in each bag at first.

I haven't been able to solve this problem without setting up equations and solve for the unknowns yet. I'll keep trying, and at the same time want to share this good problem here at MHB.

Instead of going forward I would go backwards.

Just for notation not algebra let sand in A be a , in B be b, in C be c,

at the end because all are equal we have

a = 120, b = 120, c = 120

In the last step 1/5 of sand in C was poured into A. So in C remained was 4/5 .

now 4/5 is 120 so it was 120 * 5 / 4 or 150 before .

because it was 30 poured from C to A before last step we have

a = 90, b = 120, c = 150

similarly you can calculate other 2 steps.

## 1. How do you determine the amount of sand in each bag?

To find the amount of sand in each bag, you will need to weigh the bag of sand and subtract the weight of the empty bag. This will give you the weight of the sand in the bag. Alternatively, you can also measure the volume of the sand in the bag using a measuring cup or container.

## 2. What is the best method for accurately measuring the amount of sand in each bag?

The most accurate method for measuring the amount of sand in each bag is by using a scale to weigh the bag and subtracting the weight of the empty bag. This will give you the exact weight of the sand in the bag. Measuring by volume can also be used, but it may not be as precise.

## 3. Can the amount of sand in each bag vary?

Yes, the amount of sand in each bag can vary depending on factors such as the size and density of the sand particles, the manufacturing process, and any settling that may occur during transportation. It is important to weigh or measure each bag individually to get an accurate amount.

## 4. How can I ensure that each bag has the same amount of sand?

To ensure that each bag has the same amount of sand, you can use a measuring cup or container to scoop and fill each bag with the same amount of sand. You can also use a scale to weigh each bag and adjust the amount of sand accordingly.

## 5. Can I estimate the amount of sand in each bag without weighing or measuring?

It is not recommended to estimate the amount of sand in each bag without weighing or measuring, as this can lead to inconsistencies and inaccuracies. It is best to use a scale or measuring cup to get an exact amount of sand in each bag.

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