Question 1207798: Rico's and Maris's age gap is 25 years.
4 years from now, Rico's age will be 5 years less than twices maris's age
Found 6 solutions by MathLover1, josgarithmetic, ikleyn, greenestamps, MathTherapy, mccravyedwin:
Answer by MathLover1(20850)   (Show Source):
Answer by josgarithmetic(39618)  (Show Source):
Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
Rico's and Maris's age gap is 25 years.
4 years from now, Rico's age will be 5 years less than  twice maris's age.
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The question absents, which is  .
In the post by @MathLover1, the solution is not complete.
I came to bring a complete analysis.
As you read the problem, it produces two equations.
|R-M| = 25 (1) ("the gap is 25 years")
R+4 = 2(M+4)-5 (2) ("4 years from now")
Notice that equation (1) is an absolute value equation.
So, equation (1) is equivalent to system of two equations
R - M = 25 (1a)
or
R - M = -25 (1b)
It means that we should consider two cases and solve two associated systems.
One system is
R - M = 25, (1a)
R + 4 = 2(M+4)-5. (2)
Another system is
R - M = -25, (1b)
R + 4 = 2(M+4)-5. (2)
Let start solving first system.
From equation (2),
R = 2M - 1. (3)
Substitute it into equation (1a)
(2M-1) - M = 25.
It implies
2M - M = 25 + 1
M = 26.
Substitute it into equation (3)
R = 2M - 1 = 2*26 - 1 = 51.
So, Maris is 26 years old; Rico is 51 years old.
At this point, we complete working with the first system and start working with the second system.
We again substitute (3) into equation (1b)
(2M-1) - M = -25
M = -25 + 1 = -24.
The age is always positive, it can not be negative, so we deny this possibility, at all.
ANSWER. The problem has a unique solution: Maris is 26 years old; Rico is 51 years old.
Solved in full and completely.
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The lesson to learn.
The term " gap between two values " means the absolute value of the difference.
So, the system of equations should include an absolute value equation.
In some sense, this problem is a TRAP, and if you did not recognize this trap
with the absolute value equation, then you failed.
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Added later, after seeing comment by @greenestamps to my solution.
The problem says
Rico's and Maris' age gap is 25 years.
4 years from now, Rico's age will be 5 years less than twice maris' age.
In his comment, @greenestamps writes " the information in the second sentence tells you that Rico is older".
But the problem does not say it explicitly. It says something different.
It becomes clear not from this sentence, but from analysis of the full system of equations.
So, the meaning of this @greenestamps' comment is dark to me.
I do not agree with it, and I do not think that it is correct.
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To post by Edwin.
Edwin, can you explain, please, how your post helps us to treat this problem ?
Edwin, offhand I requested Google for these keywords
"Rico's and Maris's age gap is 25 years.
4 years from now, Rico's age will be 5 years less than twices maris's age".
I got several references/links
https://math.he.net/question/1d4c2a3ddd3855cf85182d952bc3247db2813e73
https://www.facebook.com/photo.php?fbid=997207245743634&id=100063631043464&set=a.518642723600091
https://www.gauthmath.com/solution/1805163005838341/Maris-and-Rico-announced-their-breakup-Many-assume-that-the-reason-for-the-break
https://www.gauthmath.com/solution/1805071070479366/PROBLEM-Maris-and-Rico-announced-their-breakup-Many-assume-that-the-reason-for-t
So, I am very far from assuming that poor unfortunate foreign visitors send
this problem everywhere in the Internet out of curiosity and desire for knowledge.
My hypothesis is that they either participate in training AI or
fill some other web-sites this way by collecting solutions from everywhere.
All what they really do, is copying, pasting and submitting, without reading;
therefore, they even do not notice when they miss the question.
They simply do not read what they post.
Because making sense is not a goal of their job, at all.
Their job is copy/paste/submit and do it fast - nothing more.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The age gap will always be 25 years....
From the given information....
Let x = Maris's age 4 years from now
Then 2x-5 = Rico's age 4 years from now
The difference in ages 4 years from now (and always) is 25 years:
(2x-5)-x=25
2x-5-x=25
x=30
Maris's age 4 years from now: x = 30
Rico's age 4 years from now: 2x-5 = 55 (or x+25 = 55)
We don't know what the answers are, because you didn't ask a question....
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Added later, after seeing other responses....
In the editorial comment at the end of her response, tutor @ikleyn implies that you have failed to solve the problem correctly if you didn't use an absolute value equation to represent the given information that the "age gap is 25 years".
That is not true, because the information in the second sentence tells you that Rico is older. So, assuming you read the whole question before starting the work of solving the problem, an absolute value equation is not needed.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Rico's and Maris's age gap is 25 years.
4 years from now, Rico's age will be 5 years less than twices maris's age
The CORRECT answer, whatever that may be, DEPENDS on whether
"4 years from now, Rico's age will be 5 years less than twices maris's age," should acually be:
4 years from now, Rico's age will be 5 years less than twices maris's twice Maris' age, THEN
OR
4 years from now, Rico's age will be 5 years less than twices maris's twice Maris' CURRENT age
If the former, current ages are 26 and 51
If the latter, current ages are 34 and 59, with Rico OBVIOUSLY being older (2nd sentence confirms this).
Answer by mccravyedwin(407)  (Show Source):
You can put this solution on YOUR website!
I suspect that a lot of grammatical and spelling errors we find in
these problems posted on here are not due to students' carelessness.
I think it may be because these students live in a country where
English is not the main language, and they are translating their
problems from their language into English as best they can.
Edwin
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