Question

How do you find a number which exceeds 10 by as much as twice the number exceeds 38?

Answer 1

Write an equation: `2x-38 = x-10`

Solve it to find `x=28`

Explanation:

Let the unknown number be `x`

Twice the number exceeds (is more than) 38.
This difference can be written as: `2x-38`

The number exceeds 10.
This difference can be written as:`x-10`

The two differences are equal to each other.

You can now write an equation showing this information.

`2x-38 = x-10" "larr` now solve the equation for `x`

`2x-x = -10+38`

`x =28" "larr` This is the number

Let's check:

`2xx28-38 = 18`

`28-10 = 18`

The differences are the same.

Answer 2

Depending upon how you translate the given statement,
the number is either `28` or `66`.
(see below)

Explanation:

Let the number be represented by the variable `n`

There are two possible interpretations of the given statement:

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Interpretation 1

`color(red)("a number which exceeds 10")color(green)(" by as much as")color(blue)(color(magenta)(" twice the number")" exceeds 38")`

`color(red)("a number which exceeds 10 ")color(green)(=)color(blue)(color(magenta)(" twice the number")" exceeds 38")`

`color(red)(n-10)color(green)(=)color(blue)(color(magenta)(" twice the number")" exceeds 38")`

`color(red)(n-10)color(green)(=)color(blue)(color(magenta)(2n)" exceeds 38")`

`color(red)(n-10)color(green)(=)color(blue)(color(magenta)(2n)-38)`

Subtract `n` from both sides
`-10=n-38`

Add `38` to both sides
`28=ncolor(white)("XXXX")or n=28`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Interpretation 2

`color(red)("a number which exceeds 10")color(green)(" by as much as")color(blue)(color(magenta)(" twice")" the number exceeds 38")`

`color(red)("a number which exceeds 10 ")color(green)(=)color(blue)(color(magenta)(" twice")" the number exceeds 38")`

`color(red)(n-10)color(green)(=)color(blue)(color(magenta)(" twice")" the number exceeds 38")`

`color(red)(n-10)color(green)(=)color(blue)(color(magenta)("twice ")n-38)`

`color(red)(n-10)color(green)(=)color(blue)(color(magenta)2(n-38)`

Expanding the right side
`color(red)(n-10)= 2n-76`

Subtract `n` from both sides
`-10=n-76`

Add `76` to both sides
`66=ncolor(white)("XXXX")or n=66`