text: ## William says to Gracie, “If you give me \$7.50,we will have and equal amount of money. “Grace responds, “That may be true, but if you give me
  
  Question
  
  William says to Gracie, “If you give me \$7.50,we will have and equal amount of money. “Grace responds, “That may be true, but if you give me \$ 7.50 instead, I will have twice as much money as you. “How much money did William and Grace each have in the beginning? Please show work
  
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  2 weeks 2022-01-11T15:21:27+00:00 1 Answer 0 views 0
  
  ## Answers ( )
  
  1. William had \$37.5 and Gracie had \$52.5 in the beginning
  
  Step-by-step explanation:
  
  William says to Gracie:
  
  • “If you give me \$7.50, we will have an equal amount of money”
  
  Grace responds:
  
  • “That may be true, but if you give me \$ 7.50 instead, I will have twice as much money as you”
  
  Assume that William has \$x and Gracie has \$y at the beginning
  
  ∵ William has \$x
  
  ∵ Gracie has \$y
  
  ∵ When Gracie gives William \$7.5, they will have the same
  
  amount of money
  
  – That means subtract 7.5 from Gracie and add 7.5 to William
  
  and equate the two answers
  
  ∴ x + 7.5 = y – 7.5
  
  – Subtract 7.5 from both sides
  
  x = y – 15 ⇒ (1)
  
  ∵ When William gives Gracie \$7.5, Gracie will have twice as
  
  much money as William
  
  – That means add 7.5 to Gracie and equate the sum
  
  by 2 times the difference of William and 7.5
  
  ∴ y + 7.5 = 2(x – 7.5)
  
  ∴ y + 7.5 = 2x – 15
  
  – Subtract 7.5 from both sides
  
  y = 2x – 22.5 ⇒ (2)
  
  Now we have system of equations to solve it
  
  Substitute y in equation (1) by equation (2)
  
  ∵ x = 2x – 22.5 – 15
  
  – Add the like terms in the right hand side
  
  ∴ x = 2x – 37.5
  
  – Subtract 2x from both sides
  
  ∴ – x = -37.5
  
  – Divide both sides by -1
  
  x = 37.5
  
  – Substitute the value of x in equation (2) to find y
  
  ∵ y = 2(37.5) – 22.5
  
  y = 52.5
  
  William had \$37.5 and Gracie had \$52.5 in the beginning
  
  Learn more:
  
  You can learn more about the system of equations in brainly.com/question/2115716
  
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