10. Find the value of x in the equation 2(x - 3) + 5x = 5(2x + 6).
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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:
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:
Cross-multiply and divide: 5x = 7(4635) or y = $6,489
Total amount = $6,489 + $4,635 + $7,416 = $18,540