Question

Seven times a whole number decreased by twice the sum of the number and eight is equal to four times the number increased by 20.

Answer 1

Let N be a whole number.

The phrase "seven times a whole number" can be written as: 7N.

The phrase "twice the sum of the number and eight" can be written as 2(N+8).

This means that the phrase "seven times a whole number decreased by twice the sum of that number and eight" may be written as:

$7N-2(N+8)$

On the other hand, the phrase "four times the number increased by 20" translates to:

$4N+20$

Since those two expressions are related through the expression "is equal to", then we can write an equation:

$7N-2(N+8)=4N+20$

To solve this equation, use the distributive property to rewrite -2(N+8) as -2N-16:

$7N-2N-16=4N+20$

Sum like terms on each side of the equation:

$5N-16=4N+20$

Add 16 to both sides of the equation:

$5N=4N+20+16$

Add 20+16:

$5N=4N+36$

Substract 4N from both sides of the equation:

$5N-4N=36$

Add the like terms 5N and -4N:

$N=36$

Substitute N=36 in the original equation to check this answer:

$\begin{gathered} 7(36)-2(36+8)=4(36)+20 \\ \Rightarrow \\ 252-2(44)=144+20 \\ \Rightarrow \\ 252-88=164 \\ \Rightarrow \\ 164=164 \end{gathered}$