Three trade share some bags of rices in the ratio of 2:3:4 if the smallest share is 14bags find the other shares
14 = 2*7, so
2:3:4 = 14:21:28
Why did the rice traders get into a disagreement? Because they couldn't agree on the bag ratio! Anyway, let's solve the math puzzle.
If the smallest share is 14 bags, we can set up the proportion:
2:3:4 = 14:b:c.
To find the value of b, we can cross multiply and solve for it:
2 * c = 3 * 14
2 * c = 42
c = 42 / 2
c = 21.
So, the other shares are 14 bags, 21 bags, and 28 bags, in the ratio of 2:3:4.
To find the other shares, let's use the information given in the problem:
The ratio of the shares is 2:3:4, and the smallest share is 14 bags.
Let's first find the value of one share in the given ratio. We can do this by dividing the number of bags by the ratio:
The value of one share = 14 bags ÷ 2 = 7 bags.
Now, we can find the other shares using the ratio and the value of one share:
Second share = 7 bags × 3 = 21 bags.
Third share = 7 bags × 4 = 28 bags.
Therefore, the three shares are 7 bags, 21 bags, and 28 bags.
To find the other shares, we first need to determine the total number of bags of rice that the three traders have.
Let's assume the smallest share, which is 14 bags, corresponds to the ratio value of 2.
Now, we can set up a proportion to find the total number of bags.
If 2 is to 14 as (2 + 3 + 4) is to the total number of bags, we can write it as:
2/14 = (2 + 3 + 4)/x
To solve for x, we can cross multiply:
2x = 14 * (2 + 3 + 4)
2x = 14 * 9
2x = 126
Divide both sides by 2 to isolate x:
x = 126/2
x = 63
Therefore, the total number of bags of rice shared among the three traders is 63.
Now, let's find the shares for each trader based on the given ratio (2:3:4).
Trader 1's share:
2 parts out of 2 + 3 + 4 = 9 parts
Trader 1's share = (2/9) * 63 = 14 bags
Trader 2's share:
3 parts out of 2 + 3 + 4 = 9 parts
Trader 2's share = (3/9) * 63 = 21 bags
Trader 3's share:
4 parts out of 2 + 3 + 4 = 9 parts
Trader 3's share = (4/9) * 63 = 28 bags
Therefore, the shares for the three traders are:
Trader 1: 14 bags
Trader 2: 21 bags
Trader 3: 28 bags