bblast wrote:If Brian's age is exactly one-third of Tanya's age, what is Brian's age?
(1) Six years ago, Brian's age was exactly one-fifth of Tanya's age now.
(2) Twelve years from now, Brian's age will be exactly one-half of Tanya's age now.
OA-D
can someone solve this by the matrix method ?
Hi bblast!
Can you please check the wording of this problem with the original source, because currently it is incorrect (the two statements do not agree). [See matrix method below]
Statement (1):
This compares Brian's age 6 years ago with Tanya's age NOW (See below, I believe the NOW is incorrect). So Brian 6 years ago was (1/5)T. But if Brian = (1/3)T now, then 6 years ago, he will be (1/3)T - 6, so we can set them equal and solve:
(1/5)T = (1/3)T - 6
6 = (2/15)T
T = 45
B = T/3 = 15
Statement (2);
This compares Brian's age IN 12 YEARS with Tanya's age NOW (see below, I believe the NOW is incorrect)
Now we see that in 12 years Brian is 1/2 T. But if Brian = (1/3)T now, then in 12 years he will be (1/3)T - 6, so we can set them equal and solve:
(1/2)T = (1/3)T + 12
(1/6)T = 12
T = 72
B = T/3 = 24
Notice that the Statements DO NOT MATCH. @Clock60, your intuition below was exactly right and I suspect that you worked the math for the correct question:
clock60 wrote:
hi, my try
if b=1/3*t find b-?
(1)(b-6)=1/5*(t-6), solving together with t=3*b, results in b=12
(2)(b+12)=1/2*(t+12), also results in b=12
The work you are showing would be correct if the question were written as follows:
If Brian's age is exactly one-third of Tanya's age, what is Brian's age?
(1) Six years ago, Brian's age was exactly one-fifth of Tanya's age.
(2) Twelve years from now, Brian's age will be exactly one-half of Tanya's age.
Note that the difference between this version and that posted by the OP is the deletion of the word "now" at the end of each sentence.
Completing the version above with the box would be as follows:
Start with a blank box, with dates from the problem (Now, 6 years ago, 12 years from now), and fill in the info from the stem ONLY: Now, Brian is (1/3)T.
Statement (1):
6 years ago, Brian was (1/5) of Tanya's age (then). Because the Table is in T, move T into the past 6 years (T-6). Then set up Brian as (1/5) of that.
We also know that if Brian is (1/3)T now, 6 years ago he was (1/3)T - 6, so we can set that equal to what we have in the box:
(1/5)(T-6) = (1/3)T - 6
(1/5)T - 6/5 = (1/3)T - 6
6 - 6/5 = (1/3)T - (1/5)T
24/5 = (2/15)T
T = 36
B = (1/3)T = 12
Statement (2);
12 years from now, Brian will be (1/2) of Tanya's age (then). Because the Table is in T, move T into the future 12 years (T+12). Then set up Brian as (1/2) of that.
We also know that if Brian is (1/3)T now, in 12 years ago he will be (1/3)T + 12, so we can set that equal to what we have in the box:
(1/2)*(T+12) = (1/3)T + 12
(1/2)T + 6 = (1/3)T + 12
(1/2)T - (1/3)T = 6
(1/6)T = 6
T = 36
B = (1/3)T = 12
Hope this helps!!
Whit
