Bill found that if the product of 4 and a number is increased by 6, the result is 4 more than the product of 2 and the number. What is the number?

1 Answer
Jan 30, 2018

The number is #-1#

Explanation:

A product is the answer from multiplying.
The word 'AND' tells you which numbers are being multiplied.

We have two parts to the statement.

Let the number being referred to be #x#, and write an expression.

#color(blue)("the product of 4 and a number, is increased by 6"#
#color(blue)(4xx x +6)#

#color(red)("4 more than, the product of 2 and the number"#
#color(red)(4+2xx x)#

The two statements are equal, so we can write an equation:

#color(blue)(4x+6) = color(red)(4+2x)#

#4x -2x = 4-6#

#2x =-2#
#x =-1" "larr# this is the number.

Check:

#color(blue)("the product of 4 and a number is increased by 6"#
#color(blue)(4xx (-1) +6 =2)#

#color(red)("4 more than the product of 2 and the number"#
#color(red)(4+2xx (-1)=4-2 =2)#