SOLUTION: Please help me with this math issue: Mr. and Mrs. Johnson have 3 children; a son called Andy and two daughters Mary and Rosanna whom are twins and three years younger than Andy.

Question 467321: Please help me with this math issue:
Mr. and Mrs. Johnson have 3 children; a son called Andy and two daughters Mary and Rosanna whom are twins and three years younger than Andy. Mrs. Johnson is 4 years younger than her husband and next year she will be the same age as all her children together. The total age of the Johnson family now equals to 125 years.
What is the age of every family member of the Johnson family?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Mr. and Mrs. Johnson have 3 children;
a son called Andy and two daughters Mary and Rosanna whom are twins and three years younger than Andy.
Mrs. Johnson is 4 years younger than her husband and next year she will be the same age as all her children together.
The total age of the Johnson family now equals to 125 years.
What is the age of every family member of the Johnson family?
:
Let a = Andy's
Let m = Mary's age
let r = Rosanna's age
let j = Mr Johnson's age
let w = Mrs Johnson's age
:
Write an equation for each statement:
:
"a son called Andy and two daughters Mary and Rosanna whom are twins and three years younger than Andy."
m = a - 3
r = a - 3
;
" Mrs. Johnson is 4 years younger than her husband "
w = j - 4
or
j = w + 4
:
"next year she will be the same age as all her children together."
w + 1 = (a+1) + (m+1) + (r+1)
w = a + m + r + 3 - 1
w = a + m + r + 2
Replace m and r with (a-3)
w = a + (a-3) + (a-3) + 2
w = 3a - 6 + 2
w = 3a - 4
:
"The total age of the Johnson family now equals to 125 years."
j + w + a + m + r = 125
Replace j with (w+4), m & r with (a-3)
(w+4) + w + a +(a-3) + (a-3) = 125
2w + 3a + 4 - 3 - 3 = 125
2w + 3a - 2 = 125
2w + 3a = 125 + 2
2w + 3a = 127
Replace w with (3a-4)
2(3a-4) + 3a = 127
6a - 8 + 3a = 127
9a = 127 + 8
9a = 135
a =
a = 15 yrs is Andy's age
then, obviously
Mary and Rosanna are 12 yrs old
:
Find w:
w = 3(15) - 4
w = 41 yrs is wife's age
then, obviously:
45 yrs is Mr Johnson's age
:
:
See if this works out by finding the total of all the ages:
45 + 41 + 15 + 12 + 12 = 125
:
Summarize
Mr Johnson is 45
Mr's Johnson is 41
Andy is 15
Mary is 12
Rosanna is 12
o

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