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

2 Answers
Dec 28, 2016

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.

Dec 28, 2016

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:

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

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#