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

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

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Answer 1 · 2016-12-28T18:12:06

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

Solve it to find $x = 28$ $x=28$

Explanation:

Let the unknown number be $x$ $x$

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

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

The two differences are equal to each other.

You can now write an equation showing this information.

$2 x - 38 = x - 10 \leftarrow$ $2x-38 = x-10" "larr$ now solve the equation for $x$ $x$

$2 x - x = - 10 + 38$ $2x-x = -10+38$

$x = 28 \leftarrow$ $x =28" "larr$ This is the number

Let's check:

$2 \times 28 - 38 = 18$ $2xx28-38 = 18$

$28 - 10 = 18$ $28-10 = 18$

The differences are the same.

Answer 2 · 2016-12-28T18:14:38

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

Explanation:

Let the number be represented by the variable $n$ $n$

There are two possible interpretations of the given statement:

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

Interpretation 1

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

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

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

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

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

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

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

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

Interpretation 2

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

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

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

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

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

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

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

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

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

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