Uju N.
asked • 03/13/17need some help
Three insurance companies, A, B, and C, agree to jointly insure a cargo ship for $28,600,000. They allocate the premiums received in the ratio 7 : 3 : 12 respectively. How will the annual premium of $638,000 be distributed to the three insurers?
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1 Expert Answer
Gene G. answered • 03/13/17
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Retired Electrical Engineer - Setting Your Foundation for Math
In a ratio like this, there is also a total of the individual parts.
We have A:B:C:T
Where T is A+B+C
Make a table
Ratio Proportional
A 7
B 3
C 12
T 22 638,000
7 out of 22 will go to A, 3 out of 22 to B, and 12 out of 22 to C.
You can work with any two rows to make a proportion. Since the only part we know in the Proportion column is T, that row is part of the proportion you need to start with.
You can now solve for A using rows A and T:
A:T = 3:22 = A:638,000
Write these as fractions and cross multiply to solve for A.
Now you can use row A or row T with either of the other two rows to find the next answer.
Do it one more time to get the last one.
I think you can probably handle it from here. Add a comment if you need more help.
I think you can probably do it from here. Add a comment if you need more help.
Uju N.
That's really confusing
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03/13/17
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Gene G.
A proportion is just two ratios that are equal to each other.
Simple example:
GIVEN: The ratio of boys to girls in a class is 3:4.
That means for every 3 boys, there are 4 girls.
That also means that out of each group of 7 students, 3 will be boys and 4 will be girls.
You have to add the 3 and the 4 to get that 7.
TYPICAL QUESTION.
If there are 14 students in the class, how many boys and how many girls are there?
To find the number of boys, you need the ratio of boys to the total. That's B:T = 3:7
You'll write that ratio as a fraction: 3/7
The ratio for the whole class has to be the same as this, but we only know the total students.
B/T = B/14
This has to be equal to 3/7, so write the equation:
B/14 = 3/7 Solve this for B.
CROSS MULTIPLY:
_B_ = _3_
14 7
7B = 3*14
7B = 42
B = 6
Your problem has more than two parts (A, B, and C) and you had to add the parts to get a total (T).
You can only work with two of these four numbers at a time to make a ratio.
The left column represents the numbers for the ratios you were given.
The right column is the numbers for the equivalent ratios for the total (638,000). We need to find what values for A,B and C will make the ratios equal.
To find A, use the numbers for A:T from the left column to make a ratio (7:22) and set that equal to the unknown A to the total from the right column (A:638,000 = 7:22)
Solve by CROSS MULTIPLICATION.
___A___ = __7_
638000 22
22A = 7*638000
22A = 4466000
A = 203,000
Do the same for B:
B / 638000 = 3 / 22
22B = 3*638000
22B = 1914000
B = 87,000
And for C:
C / 638000 = 12 / 22
22C = 12*638000
22C = 7656000
C = 348,000
03/14/17