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