One number is 2/3 of another number. The sum of the two numbers is 10. How do you find the two numbers?

2 Answers
Suren Abreu · EZ as pi
Oct 26, 2016

The two numbers are #4# and #6#.

Explanation:

Let one number be represented as #x# and the other as #y#.

According to the problem:

#x=2/3y# and #x+y=10#

From the second equation we get:

#x+y=10#

#:.color(red)(y=10-x)# (subtracting #x# from both sides)

Replacing the value of #y# in the first equation we get:

#x=2/3color(red)(y)#

#x=2/3color(red)((10-x))#

Multiplying both sides by #3# we get:

#3x=2(10-x)#

Opening the brackets and simplifying we get:

#3x=20-2x#

Add #2x# to both sides.

#5x=20#

Divide both sides by #5#.

#x=4#

Since from the second equation we have:

#x+y=10#

substituting #x# with #4# we get:

#4+y=10#

Subtract #4# from both sides.

#y=6#

EZ as pi
Oct 26, 2016

The numbers are 4 and 6.

Explanation:

This question can also be done by using just one variable.
Define each variable and then form an equation.

Let the larger number be #x#.
The other number is #2/3x#

The sum of the numbers is 10.

#x+2/3x = 10" "larr# multiply by 3

#3x + (3xx2x)/3 = 30#

#3x + 2x = 30#

#5x = 30#

#x = 30/5= 6" "larr#this is the larger number

#2/3 (6) = 4" "larr# this is the smaller number.

The numbers are 4 and 6.

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