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We are going to go back to
Question 3 and go through it in detail. Note as we
do it that the process follows the same pattern on
each of the questions.
First, read the
question.
Question 3:
Next year
Paul will be twice the age of Harry. Eric is three
years older than Paul. There total ages are 76.
What are each of their ages ?
You've got it, we're going to
read it again.
Next year
Paul will be twice the age of Harry. Eric is three
years older than Paul. There total ages are 76.
What are each of their ages ?
There are THREE people
involved in this question, Paul, Harry and Eric,
but we handle it just the same.
This time it's about how old
each of them is.
The question tells us three
things.
1. - That NEXT YEAR Paul will
be twice the age of Harry.
2. - That Eric is three years
older than Paul
3. - That their combined ages
add up to 76
The question wants us to
determine how old each of them is.
The
first
thing we do is
identify the person we
don't
know anything about.
That's Harry isn't it?
Because we know something about Paul and
Eric.
So after the question we
write
this line:
Let 'x' equal
the age of
Harry.
The 'x'
represents a number but at this stage we don't know
what the number is.
Algebra is a
way to find out that number from the other data we
are told.
Harry - We've
already decided that Harry is 'x' years old.
Paul -
since
NEXT YEAR he will be
twice the age of
Harry,
therefore Paul is (2x -1) The -1 comes from the
statement that it's not unitl NEXT YEAR that he's
twice as old, so THIS YEAR he is one year younger
than that. This is written as (2x - 1). We'll keep
the brackets around it at the moment.
Eric - is 3 years older than Paul. That makes Eric
(2x - 1) + 3 years old.
We can now
write this in the form of an equation and then
solve
it:-
(An
equation means just two things that are equal). The
equation is solved using the same means as in
normal arithmatic.
s
The equation
is as follows:
Their combined ages = Harry's
age + Paul's age + Eric's age
Written
numerically this becomes:
-
Combined-----
-
Harry
---Paul----Eric
----
-- - --
---\----
/
/-- -
- - -
-
/- -
-.......
/-
----------------
76 =
x + (2x - 1) + (2x -1) +
3--------
----------------
76 = x + 2x -1 + 2x -1 +3
.....(In
this case we can just remove the brackets)
-
--
------.............
76 =
5x +1
---.........
(Add
the x's and numbers together)
------.......
76 -
1 =
5x......
-----..(Subtract
1 from both sides to get just 'x's on one
side)
--(--
------.............
75 =
5x
-----........76
÷ 5 =
x--------(We
now divide each side by 5 to get a single
'x')
----------
--..--15
=
x------Who
did we say 'x' was?
Click on the answer below you
believe is the correct one.
Answer to
question 3:
A' - Harry
is 14, Paul is 28, Eric is 31
'B' -
Harry
is 15, Paul is 29, Eric is 32
'C' -
Harry
is 16, Paul is 30, Eric is 33
'D' -
Harry
is 17, Paul is 31, Eric is 34
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