If the sum of the number is 17 2/3 and one number is 6 3/5 find the other number
Answers
Let's write these as equations.
"The sum of two numbers is 17."
Calling these unknown numbers
x
and
y
, we can write that:
x
+
y
=
17
Then, we see that "one number is 3 less than 2/3 of the other number."
Let's say that
y
is the "one number." If
y
is 3 less than 2/3 of
x
, this is written as:
y
=
2
3
x
−
3
From here, we have to take this equation for
y
and use it in our first equation. Since we know that
y
and
2
3
x
−
3
are equal, we can replace
y
with
2
3
x
−
3
in the first equation:
x
+
y
=
17
x
+
2
3
x
−
3
=
17
From here, we can add
x
+
2
3
x
using fractions:
x
+
2
3
x
=
3
3
x
+
2
3
x
=
5
3
x
5
3
x
−
3
=
17
Add
3
to both sides of the equation:
5
3
x
=
20
Multiply both sides by
3
5
:
x
=
20
×
3
5
=
5
(
4
)
(
3
)
5
=
12
If
x
=
12
, then
y
=
5
, since their sum is
17
.
So the two numbers are
5
and
12
.
Answer link
EZ as pi
Apr 12, 2017
The smaller number is
5
Explanation:
It is possible to define the two numbers using only one variable.
Let the smaller number be
x
The other number is
(
17
−
x
)
(We know they add up to
17
)
2
3
of the bigger number is written as:
2
3
(
17
−
x
)
The smaller number is
3
less than that. (so, subtract
3
to get
x
)
x
=
2
3
(
17
−
x
)
−
3
←
we have an equation, solve for
x
3
x
=
3
×
2
3
(
17
−
x
)
−
3
×
3
←
×
3
3
x
=
34
−
2
x
−
9
3
x
+
2
x
=
25
5
x
=
25
x
=
5
The smaller number is
5
, the larger is
12
Check:
2
3
×
12
−
3
=
8
−
3
=
5
Answer:
11 1/15
Step-by-step explanation:
17 2/3-6 3/5=11 1/15