At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Laura and drew went shopping together. Ratio of money laura brought to the money drew brought was 5:7. After they each spent $76, the ratio od money they had left was 3:5. How much more money does Drew have than Laurah

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.

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.