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
