These kinda ?s always stump me.?

Question

Mary's and Bob's ages combined are twice Jane's age. Mary is 8 years older than Bob. Jane's age plus Bob's age is 20 years. How old are they?

Answer 1

Let M = Mary's age
Let B = Bob's age
Let J = Jane's age

"Mary and Bob's ages combined are twice Jane's age"
M + B = 2J

"Mary is 8 years older than Bob"
M = B + 8

"Jane's age plus Bob's age is 20 years"
J + B = 20

Now you have 3 equations and 3 unknowns... can you take it from here?

Let's try substitution. Notice how equation two tells us what M equals (in terms of B), so replace M with B + 8 in the first equation:

M + B = 2J
(B + 8) + B = 2J

Combine the B terms:
2B + 8 = 2J

Divide everything by 2:
B + 4 = J
J = B + 4

Okay, now substitute the value of J = B + 4 into the last equation:
J + B = 20
(B + 4) + B = 20

Combine B terms:
2B + 4 = 20

Subtract 4 from both sides:
2B = 16

Divide both sides by 2:
B = 8

So now you know Bob is 8. Use this to determine the other ages:
J = B + 4
J = (8) + 4
J = 12
Jane is 12.

Finally solve for M:
M = B + 8
M = (8) + 8
M = 16
Mary is 16.

Double check your answers:

Mary and Bob's ages combined (24) are twice Jane's age (2 x 12). Check
Mary (16) is 8 years older than Bob (8). Check
Jane's age (12) plus Bob's age (8) is 20 years. Check.

In summary:
Bob is 8
Jane is 12
Mary is 16

Answer 2

M + B = 2J
M = B + 8
J + B = 20

(B + 8) + B = 2J, or 2B - 2J = -8

2B - 2J = -8
2B + 2J = 40

4B = 32
B = 8

M = B + 8 = 16
J + B = 20, so J =12

B=8, M=16, J=12