3. Sarah is twice as old as John. Six years ago Sarah was four times as old as John was then. In years, how old is John now?

A)   3
B)   9
C) 18
D) 20
E) Cannot be determined

Answer:

A) Did you translate "four times as old as John was then" to 4J? You would have gotten 2J – 6 = 4J and been careless by saying that J = 3. Wrong translation, and careless use of math rules. Choice B is correct. Here is the best way:

Use Strategy 2, p. 71; BASIC SKILLS - Mini Math Refresher - Rule, p. 157; Equations, p. 158; Math Refresher (407), p. 244: You won't rack your brains if you know how to translate from words to math. Translate Sarah to S, John to J, "is" to =, six years ago to – 6, four times as old as John was then to 4 (J – 6). Then "Sarah is twice as old as John" translates to

1) S = 2J.

And "six years ago, Sarah was 4 times as old as John was then" translates to

2) S – 6 = 4(J – 6) , the reason for J – 6 because John was J – 6, six years ago.

Substituting S = 2J in Equation 1, in Equation 2, we get

2J – 6 = 4(J – 6).

Then we get:

2J – 6 = 4J – 24.

And then:

– 6 + 24 = 4J – 2J = 2J.

So

2J = 18 and J = 9.

B) You are right! Choice B is correct. Here is the best way:
Use Strategy 2, p. 71; BASIC SKILLS - Mini Math Refresher - Rule, p. 157; Equations, p. 158; Math Refresher (407), p. 244:

You won't rack your brains if you know how to translate from words to math.Translate Sarah to S, John to J, "is" to =, Six years ago to – 6, four times as old as John was then to 4 (J – 6). Then "Sarah is twice as old as John" translates to

(1) S = 2J.

And "six years ago, Sarah was 4 times as old as John was then" translates to

(2) S – 6 = 4(J – 6) , the reason for J- 6 because John was J – 6, six years ago.

Substituting S = 2J in Equation 1, in Equation 2, we get

2J – 6 = 4(J – 6).

Then we get:

2J – 6 = 4J – 24.

And then:

– 6 + 24 = 4J – 2J = 2J.

So

2J = 18 and J = 9.

C) Did you solve for Sarah's age (S) and get S= 18 or did you get for Johns's age (J), 2J = 18 and choose 18 as the answer? Choice B is correct. Here is the best way:
Use Strategy 2, p. 71; BASIC SKILLS - Mini Math Refresher - Rule, p. 157; Equations, p. 158; Math Refresher (407), p. 244:

You won't rack your brains if you know how to translate from words to math.Translate Sarah to S, John to J, "is" to =, Six years ago to – 6, four times as old as John was then to 4 (J – 6). Then "Sarah is twice as old as John" translates to

(1) S = 2J.

And "six years ago, Sarah was 4 times as old as John was then" translates to

(2) S – 6 = 4(J – 6) , the reason for J- 6 because John was J – 6, six years ago.

Substituting S = 2J in Equation 1, in Equation 2, we get

2J – 6 = 4(J – 6).

Then we get:

2J – 6 = 4J – 24.

And then:

– 6 + 24 = 4J – 2J = 2J.

So

2J = 18 and J = 9.

D) That is incorrect. Choice B is correct. Here is the best way:
Use Strategy 2, p. 71; BASIC SKILLS - Mini Math Refresher - Rule, p. 157; Equations, p. 158; Math Refresher (407), p. 244:

You won't rack your brains if you know how to translate from words to math.Translate Sarah to S, John to J, "is" to =, Six years ago to – 6, four times as old as John was then to 4 (J – 6). Then "Sarah is twice as old as John" translates to

(1) S = 2J.

And "six years ago, Sarah was 4 times as old as John was then" translates to

(2) S – 6 = 4(J – 6) , the reason for J- 6 because John was J – 6, six years ago.

Substituting S = 2J in Equation 1, in Equation 2, we get

2J – 6 = 4(J – 6).

Then we get:

2J – 6 = 4J – 24.

And then:

– 6 + 24 = 4J – 2J = 2J.

So

2J = 18 and J = 9.

E) That is not correct. You can obtain two equations involving Sarah (S) and John (J). And you have two unknowns S and J. Unless one equation is a multiple of the other, you can determine the unknowns.