Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Last month David and Mary saved some money in a ratio of 3:5. This month they saved an additional $154 together, and David now has three times as much money as he had last month and Mary has two times as much as she had last month. How much money did they save last month?

Sagot :

sqdancefan

Answer:

  • David: $42
  • Mary: $70

Step-by-step explanation:

The two relations can be translated to a system of linear equations in two variables. These can be solved in any of the usual ways.

__

setup

Let d and m represent the amounts David and Mary saved last month, respectively.

The first relation tells us

  d/m = 3/5   ⇒   5d = 3m   ⇒   5d -3m = 0

The second relation tells us that adding 3 times what David had last month to 2 times what Mary had last month will give a total that is 154 greater than the sum of their funds last month.

  d +m + 154 = 3d +2m   ⇒   2d +m = 154

__

solution

We can add 3 times the second equation to the first to eliminate m.

  (5d -3m) +3(2d +m) = (0) +3(154)

  11d = 462 . . . . . . . . simplify

  d = 42 . . . . . . . . . divide by 11

Using the second equation, we can find Mary's savings:

  m = 154 -2d

  m = 154 -2(420 = 70

David saved $42 last month; Mary saved $70.

View image sqdancefan
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.