SOLUTION: Robert is 24 years older than pete. In 8 years, their age will equal 62. How old is Robert now?

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Question 1203440: Robert is 24 years older than pete. In 8 years, their age will equal 62. How old is Robert now?
Found 5 solutions by MathLover1, math_tutor2020, josgarithmetic, greenestamps, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let Robert ‘s age be R and Pete’s age P
if Robert is 24 years older than Pete, we have
R=P%2B24......eq.1

if in 8 years, their age will equal 62, we have
%28R%2B8%29+%2B+%28P%2B8%29=62....substitute R from eq.1
%28P%2B24%2B8%29+%2B+%28P%2B8%29=62
P%2B32+%2B+P%2B8=62
2P%2B40=62
2P=62-40
2P=22
P=11

go to eq.1
R=P%2B24......eq.1...substitute P
R=11%2B24
R=35
Robert is 35 years old now.

Answer by math_tutor2020(3817) About Me  (Show Source):
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x = Robert's age right now
x-24 = Pete's age right now

x+8 = Robert's age 8 years from now
(x-24)+8 = x-16 = Pete's age 8 years from now

(x+8)+(x-16) = 2x-8 = sum of their future ages
2x-8 = 62
2x = 62+8
2x = 70
x = 70/2
x = 35

Answer: Robert is currently 35 years old.

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A slightly different approach

x = Robert's age 8 years into the future
x-24 = Pete's age 8 years into the future

x + (x-24) = 2x-24 = sum of their future ages
2x-24 = 62
2x = 62+24
2x = 86
x = 86/2
x = 43

Robert will be 43 years old 8 years into the future.
Subtract off 8 to get his present age.
43-8 = 35

Answer: Robert is currently 35 years old.

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
r is k years older than p. In y years, their ageS will equal T. How old is R now?



Unknown variables r and p.
system%28r=p%2Bk%2Cr%2By%2Bp%2By=T%29

system%28r=p%2Bk%2Cr%2Bp=T-2y%29

system%28r-p=k%2Cp=T-2y-r%29
r-%28T-2y-r%29=k
r-T%2B2y%2Br=k
2r=k%2BT-2y
highlight_green%28r=%28k%2BT%29%2F2-y%29-----------substitute the given values.

highlight%28r=%2824%2B62%29%2F2-8%29



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All in symbols useful if you have a few or more problems which are in the same form as the example.

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Keeping the "+8" in the algebraic equation to represent the 8 years in the future makes the equation more complicated and makes the ensuing work to solve the problem harder.

Do some preliminary logical analysis to reduce the amount of the overall effort.

If in 8 years the sum of their ages will be 62, then currently the sum of their ages is 62-8-8 = 46.

Now let x be Pete's age so that x+24 is Robert's age. Then

x+(x+24)=46
2x+24=46
2x=22
x=11

Currently Pete is 11 years old, so Robert is 11+24 = 35 years old.

ANSWER: 35

Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.

This problem is intended for comparatively young students,
who do not solve problems manipulating with symbolical designations,
since they are not prepared for it, yet.

So, this and many other similar exercises by @josgarithmetic
are not appropriate for using by such students.


You may ignore his post as irrelevant to goals of this forum.


It is definitely wrong way to teach.


Perpendicular to teaching goals and all educational conceptions, strategies, approaches and methodology.


Simply saying, when a student is able to manipulate with symbolical designations,
all these "age" problems are far behind of him (or her).