Answered

John and Mike are talking about the number of pens they have. John says 'If I give you four of my pens, we will have the same number of pens'. Mike says 'If I give you five of my pens, you will have ten times as many as me'. How many pens do they each have?



Answer :

rvkacademic

Answer:

John has 15 pens and Mike has 7 pens

Step-by-step explanation:

Let us use the variable J to denote that the  initial number of pens John has and M to denote the initial number of pens Mike has.

John's statement states that if he gives Mike 4 pens then they both will have the same number of pens

  • If John gives Mike 4 pens then he will have 4 less pens which can be algebraically translated to J - 4
  • Since Mike receives 4 pens we can translate that to
    M + 4 after the transaction
  • These expressions must be equal so we have our first equation
    J - 4 = M + 4

    J = M + 8      (by adding 4 to both sides)    [1]

Mike's statement that if he gives 5 pens to John, John will have 10 times the number of pens

  • If Mike gives John 5 pens John's pen stock becomes J + 5
  • Mike's pen stock becomes M - 5
  • The statement translation into algebra becomes
    J + 5 = 10(M -5)
    J + 5 = 10M - 50            (expand parentheses)

    - Substitute J = M + 8 from equation 1:
    M + 8 + 5 = 10M - 50
    M + 13 = 10M - 50
    M + 63 = 10M     (add 50 both sides)
    63 = 9M   (subtract M both sides)
    9M = 63     (switch sides)
    M = 63/9 = 7
  • Using equation 1
    J = M + 8 => J = 7 + 8 = 15
  • This means
    John has 15 pens and Mike has 7 pens originally