Find the value of x: Solving Equations

1) Two men are decorating a room. One has painted 20m^2 and the other one only 6m^2. They continue painting and manage to paint another x m^2 each. If the first man has painted exactly three times the area was painted by the second man, find the value of x.
2) Mr Jones is 4 years older than his wife and 31 years older than his son. Their ages add up to 82 years. If Mr Jones is x years old, find the value of x and find the ages of his wife and son.

Thank you, choosing a best answer.

1) if they both paint at an identical pace after the 20m^2 and 6m^2 have been painted, then the function of the first man will be 20 + x and the second man will be 6 + x. to find when the first is 3 times then second, multiply the second by 3 and equate;

20 + x = 3*(6+x)
20 + x = 18 + 3x
2 = 2x
x = 1 m^2

2) 82 = Age of mr. Jones + age of wife + age of son
82 = x + x-4 + x-31
82 = 3x - 35
3x = 117
x = 39 years

wife = 39 years - 4 = 35 years old
son = 39 years - 31 = 8 years old

(1)
x=1 if you add 1m^2 to both figures then you end up with 21 and 7, 21 divided by 7 is three, so 1m^2 is the value of x

(2) I would use this simple method, son has to = at least 0
wife has to = at least 27
mr jones has to = at least 31
Because there are three people, the amount that you will add to 31 is (82 - (27+31)) / 3
24 divided by three is 8, so you add 8 to the ages 31, 27 and 0
meaning mr. Jones is 39, and this is also the value of x
his wife is 35
his son is 8
hope this helped :)

1. 20 + x = Amount first man has painted, total.
6+x = Amount second man has painted, total.

First = 3*second

20+x = 3(6+x)
20 + x = 18 + 3x
2x = 2
x = 1

2. x - 4 = age of wife
x - 31 = age of son

x + (x - 4) + (x - 31) = 82
3x - 35 = 82
3x = 117
x = 39

Therefore Mr. Jones is 39, his wife is 35, and his son is 8.

1) M = 20 + x
J = 6 + x
M = 3J
20 + x = 3(6 + x) = 18 + 3x
20 + x = 18 + 3x Subtract x from each side
20 = 18 + 2x Subtract 18 from each side
2 = 2x
1 = x ---> x = 1 m^2

2) J = x
W = x - 4
S = x - 31

J + W + S = 82
x + (x - 4) + (x - 31) = 82
3x - 35 = 82 Add 35 to each side
3x = 117 divide by 3
x = 39
Mr jones is 39 yrs old, His wife and 39 - 4 = 35 yrs old, his son is 39 - 31 = 8 yrs old

1.)
(20 +x)=3(6+x)
20+x=18x+3x
20-18=3x-x
2=2x
x=1m^2

2.)
Mr. Jones = x
Mrs. Jones = x-4
Child = x-31

(x) + (x-4) + (x-31) = 82
3x=117
x=39yrs

i don't know. go ask your teacher.