Step-by-step explanation:
The sum of two positive numbers is four and three times the smaller number is one more than the larger. What are the two numbers?
Explanation:
To find such a word problem, we can first note that
1.25
+
2.75
=
4
, which makes a nice easy number to refer to verbally.
In addition, note that
3
⋅
1.25
=
3.75
=
2.75
+
1
, which allows us to formulate the second part of the system.
So we can pose a question like:
The sum of two positive numbers is four and three times the smaller number is one more than the larger. What are the two numbers?
How would you solve it?
Let
x
,
y
represent the smaller and larger numbers respectively.
Then from the question:
{
x
+
y
=
4
3
x
=
y
+
1
Subtracting
y
from both sides of the second equation gives us:
3
x
−
y
=
1
Adding this to the first equation gives us:
4
x
=
5
Then dividing both sides by
4
gives us:
x
=
5
4
=
1.25
Subtracting
x
from both sides of the first equation, we have:
y
=
4
−
x
=
4
−
1.25
=
2.75
