Question

Question #09f89

Answer 1

`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`

Answer 2

`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`