To share 54 among three girls in the proportion 11:5:2, we first need to determine the total number of parts in the ratio.
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Add the parts of the ratio together:
\( 11 + 5 + 2 = 18 \) -
Now, we can find the value of each part by dividing the total amount (54) by the total number of parts (18):
\[ \text{Value of each part} = \frac{54}{18} = 3 \] -
Next, we can calculate how much each girl receives by multiplying the value of each part by the number of parts she gets according to the ratio:
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For the first girl (11 parts):
\[ 11 \times 3 = 33 \] -
For the second girl (5 parts):
\[ 5 \times 3 = 15 \] -
For the third girl (2 parts):
\[ 2 \times 3 = 6 \]
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So, the amounts received by each girl are:
- First girl: 33
- Second girl: 15
- Third girl: 6
To summarize, the distribution is:
- First girl: 33
- Second girl: 15
- Third girl: 6