Question

A sum of money was shared among Daniel Elliot and frank in the ratio 5 : 7 : 8 . If frank shares was $2,781 more than Daniel share what was the original sum of money shared among the three men?

Answer 1

Answer:

$18,540

Step-by-step explanation:

To find the original sum of money shared, setting up two different proportions using the ratios and the amount given will help.  For the first proportion, we can set 'x' equal to the amount of money that Daniel received.  Since Frank received $2,781 more than this amount, his amount is the expression 'x + 2781'.  Using equivalent ratios, we can set up the following proportion:

$\frac{Frank}{Daniel}=\frac{8}{5}=\frac{(x+2781)}{x}$

Using cross-multiplication: 8x = 5(x + 2781)

Distribute: 8x = 5x + 13,905

Inverse operations: 3x = 13,905 or x = $4,635

Since 'x' represents the amount that Daniel received, than Frank received:

x + 2781 or 4,635 + 2,781 = $7,416

To find the remaining amount for Elliot, make another proportion:

$\frac{Daniel}{Elliot}=\frac{5}{7}=\frac{4635}{y}$

Cross-multiply and divide:  5x = 7(4635) or y = $6,489

Total amount = $6,489 + $4,635 + $7,416 = $18,540