Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Answer:
$76
Step-by-step explanation:
Given the initial ratio of Laura's money to Drew's money is 5:7, and it is reduced to 3:5 after each spends $76, you want to know how much more Drew has than Laura.
Setup
Let L and D represent the money Laura and Drew have to start. The given relations tell us ...
[tex]\dfrac{L}{D}=\dfrac{5}{7}\\\\\\\dfrac{L-76}{D-76}=\dfrac{3}{5}[/tex]
Solution
Cross-multiplying each equation gives ...
7L = 5D
5(L -76) = 3(D -76)
Rearranging, we have ...
5D -7L = 0
3D -5L = -2(76)
Subtracting the second of these equations from the first gives ...
(5D -7L) -(3D -5L) = (0) -(-2)(76)
2D -2L = 2(76) . . . . . . . simplify
D -L = 76 . . . . . . . . . . . . divide by 2
Drew has $76 more than Laura.
__
Additional comment
Often, it works well to consider the ratio units. Here, the spending reduces each of the ratio units by 2: 5→3, 7→5. The initial and final difference between the ratio units are both 2: 7-5=2, 5-3=2. This suggests the difference is equal to the spending, $76.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.