Question #09f89

2 Answers
Oct 10, 2017

#99#

Explanation:

Let #x=#smaller first number and #y=#larger second number

We know that:

#y-x=30->x=y-30#

Also we know that:

#2/3x+1/11y=5#

Fraction bust this equation by multiplying every term by #33#:

#22x+3y=165#

Combine the two equations:

#22(y-30)+3y=165#

#22y-660+3y=165#

#25y=825#

#y=33#

So #x=3#

Which means the product of the two numbers is #99#

Oct 10, 2017

#ab=99#

I can't help but think they are looking for some sort of shorter method. Some sort of hidden link!

Explanation:

I am assuming you know and understand the shortcut methods.

Let the first number be #a#
Let the second number be #b#

Assuming that #b>a#

Given that: #b-a=30" "...........Equation(1)#

Given that: #2/3a+1/11b=5" ".....Equation(2)#

Instructed to determine #ab#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the values of "a and b)#

Consider #Equation(2)#

#22/33a+3/33b=165/33#

#22a+3b=165#

From #Equation(1) " "a=b-30#

Thus: #22a+3b=165color(white)("d")->color(white)("d")22b+3b-660=165#

#b=825/25=33#

Thus #Equation(1)# becomes:

#33-a=30 => a=3#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Check")#

#2/3xx(3)+1/11xx(33) -> 5# as required
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Part 2 - determine the product "ab)#

#ab=3xx33=99#