Story problem help!!?

Question

Al is 9 years younger than Jim, Bob is 3 years younger than Al, and Pat is 17 years older than Bob. How old is each if the sm of their ages is 76?????

Answer 1

A + 9 = J
B + 3 = A or A-3 = B
B + 17 = P and A + J + B + P = 76. So, A + (A+9) + (A-3) +((A-3) + 17 = 76 = 4A + 9 - 3 -3 + 17 = 4A + 20
(76-20) = 4A = 56 therefore A = 14, J=23, B=11, P =28.
14+23+11+28 = 76 QED

Answer 2

Here's the problem statement:

Jim+Al+Bob+Pat=76
J+(J-9)+(J-9-3)+(J-9-3+17)=76

Here's the work:
Reorder the terms:
J + (-9 + J) + (J + -9 + -3) + (J + -9 + -3 + 17) = 76

Remove parenthesis around (-9 + J)
J + -9 + J + (J + -9 + -3) + (J + -9 + -3 + 17) = 76

Reorder the terms:
J + -9 + J + (-9 + -3 + J) + (J + -9 + -3 + 17) = 76

Combine like terms: -9 + -3 = -12
J + -9 + J + (-12 + J) + (J + -9 + -3 + 17) = 76

Remove parenthesis around (-12 + J)
J + -9 + J + -12 + J + (J + -9 + -3 + 17) = 76

Reorder the terms:
J + -9 + J + -12 + J + (-9 + -3 + 17 + J) = 76

Combine like terms: -9 + -3 = -12
J + -9 + J + -12 + J + (-12 + 17 + J) = 76

Combine like terms: -12 + 17 = 5
J + -9 + J + -12 + J + (5 + J) = 76

Remove parenthesis around (5 + J)
J + -9 + J + -12 + J + 5 + J = 76

Reorder the terms:
-9 + -12 + 5 + J + J + J + J = 76

Combine like terms: -9 + -12 = -21
-21 + 5 + J + J + J + J = 76

Combine like terms: -21 + 5 = -16
-16 + J + J + J + J = 76

Combine like terms: J + J = 2J
-16 + 2J + J + J = 76

Combine like terms: 2J + J = 3J
-16 + 3J + J = 76

Combine like terms: 3J + J = 4J
-16 + 4J = 76

Solving
-16 + 4J = 76

Solving for variable 'J'.

Move all terms containing J to the left, all other terms to the right.

Add '16' to each side of the equation.
-16 + 16 + 4J = 76 + 16

Combine like terms: -16 + 16 = 0
0 + 4J = 76 + 16
4J = 76 + 16

Combine like terms: 76 + 16 = 92
4J = 92

Divide each side by '4'.
J = 23

Simplifying
J = 23

Jim is 23
Al is 23-9, or 14
Bob is 14-3, or 11
Pat is 11+17, or 28

23+14+11+28=76

Answer 3

1) Al = Jim - 9
2) Bob = Al - 3 = Jim - 12
3) Pat = Bob + 17 = Jim + 5
4) Al + Bob + Pat + Jim = 76

So, (Jim - 9) + (Jim - 12) + (Jim + 5) + Jim = 76
4Jim + 1 + 5 - 9 - 12 = 76; 4Jim = 76 + 15 = 91

5) Jim = 91 / 4
6) Pat = Jim + 5 = 111 / 4
7) Bob = Jim - 12 = 91 / 4 - 12 = (91 - 48) / 4 = 43 / 4
8) Al = Jim - 9 = (91 - 36) / 4 = 55 / 4

Answer 4

I believe this is an example of a Diophantine equation, although I'm a little rusty with this sort of thing. You can set it up as a system of equations, but after you've done all the substitution you can do, you still have more than one variable, and so you can't solve it in the traditional sense.

When I have solved problems of this sort in the past, I simplified it by substitution as much as possible, then I used a chart. On the chart, I list possible solutions and see which one will fit the particular circumstances of the problem. Remember, you are dealing with age, so that limits the possibilities.

Answer 5

You either trial and error or use equations

let the ages of:

Al = A
Bob = B
Pat = P
Jim = J

A=J-9
B=A-3
P=B-17

A+B+P+J = J-9+(J-9-3)+(J-9-3-17)+J =76

4J-50=76

Can you find out how old Jim is? and then the others?
i'll leave u to work it out urself