SOLUTION: The sum of two distinct numbers is 26. If the smaller number is reduced by 1 and the larger number by 3, the product of the two resulting number is 120. What are the numbers?
Question 1011602: The sum of two distinct numbers is 26. If the smaller number is reduced by 1 and the larger number by 3, the product of the two resulting number is 120. What are the numbers? Found 2 solutions by stanbon, addingup:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The sum of two distinct numbers is 26. If the smaller number is reduced by 1 and the larger number by 3, the product of the two resulting number is 120. What are the numbers?
--------------
Equations:
S + L = 26
(S-1)(L-3) = 120
------
Substitute for "S" and solve for "L"::
(26-L-1)(L-3) = 120
------
(25-L)(L-3) = 120
-----
-L^2 + 28L - 75 = 120
L^2 - 28L + 195 = 0
==============
L = 15
S = 11
-----------------
Cheers,
Stan H.
----------
You can put this solution on YOUR website! x+y= 26 so if we want y only we can subtract x from 26:
y= 26-x Remember this value for y
--------------------------------------------------
(x-1)(y-3)= 120 Let's substitute for y:
(x-1)(26-x-3)= 120
(x-1)(23-x)= 120
Do FOIL on this equation:
23x+-x^2+-23+x= 120 Simplify and re-arrange:
-x^2+24x-23= 120 Multiply both sides by -1
x^2-24x+23= -120 Add 120 on both sides
x^2-24x+143= 0 Factor this equation (FOIL) and you get:
(x-13)(x-11)= 0 Split into 2 equations:
x-13=0 or x-11= 0
x= 13 or x= 11
--------------------
Let's try these numbers and see which one is correct:
(13-1)(y-3)= 120 solve for y:
y= 13 This is not our answer, the problem clearly states "two distinct numbers" and "smaller number", "larger number".
Let's try 11:
(11-1)(y-3)= 120
y= 15 Now we have an answer:
11-1*15-3= 120
10*12= 120
120= 120 We've got the correc answer
(