If the sum of two numbers is 15 and their product is 50 what are they?

3 Answers
Jane
Feb 24, 2018

Let,the two numbers be #a# and #b#,

So, #a+b=15#...1

and, #ab=50#

so, #(a-b)^2 = (a+b)^2 - 4ab=225 - 200=25#

so, #a-b = -@+5# ...2

So,solving 1 & 2 we get, #(a=10,b=5)# or , #(a=5,b=10)#

So,the numbers are #5# and #10#

smendyka
Feb 24, 2018

See a solution process below:

Explanation:

First, let's call the two numbers: #n# and #m#

Then we can write two equations:

  • #n + m = 15#
  • #nm = 50#

Step 1) Solve the first equation for #n#:

#n + m - color(red)(m) = 15 - color(red)(m)#

#n + 0 = 15 - m#

#n = 15 - m#

Step 2) Substitute #(15 - m)# for #n# in the second equation and solve for #m#:

#nm = 50# becomes:

#(15 - m)m = 50#

#15m - m^2 = 50#

#-m^2 + 15m = 50#

#-m^2 + 15m - color(red)(50) = 50 - color(red)(50)#

#-m^2 + 15m - 50 = 0#

#-1(-m^2 + 15m - 50) = -1 * 0#

#m^2 - 15m + 50 = 0#

#(m - 10)(m - 5) = 0#

Step 3) We can now solve each term on the left for #0#

#m - 10 = 0#

#m - 10 + color(red)(10) = 0 + color(red)(10)#

#m - 0 = 10#

#m = 10#

Or

#m - 5 = 0#

#m - 5 + color(red)(5) = 0 + color(red)(5)#

#m - 0 = 5#

#m = 5#

#m = 5# or #m = 10#

Therefore:

#n = 10# or #n = 5#

There two numbers are:

#5# and #10#

#5 + 10 = 15#

#5 xx 10 = 50#

Tom M.
Feb 24, 2018

5 and 10

Explanation:

Let our two numbers be #a# and #b#

#[1]" "a+b=15#

#[2]" "ab=50#

Rearranging #[1]# we get:

#a=15-b#

Substitute this into #[2]#

#b(15-b)=50#
#15b-b^2-50=0#
#b^2-15b+50=0#
#(b-10)(b-5)=0#

So #b=10# or #b=5#

In fact, 10 and 5 are both the numbers for this, but we should check this in the top equation.

Let #b=5#

#a+5=15#
#a=10#

So 5 and 10 is a pair of solutions

Let #b=10#

#a+10=15#

#a=5#

So 5 and 10 is the other pair of solutions.

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