Chapter 6, Problem 1RVS

To determine

To calculate: The mathematical equation of the statement, “In $2014$, advertisers worldwide spent $\$16.1\text{ billion}$ on social-networking advertising. This was an $45.3\%$ increase over the amount spent in $2013$.” Also, calculate the amount spend in $2013$.

Answer to Problem 1RVS

Solution:

The mathematical model is $x+45.3\%\cdot x=16.1$ and the money spent in 2013 was $\$11.08\text{ billion}$.

Explanation of Solution

Given information:

The provided statement,

“In 2014, advertisers worldwide spent $16.1 billion on social-networking advertising. This was a 45.3% increase over the amount spent in 2013.”

Formula used:

Percentage formula.,

$x\%\text{ of }y=y\cdot \frac{x}{100}$

Calculation:

Consider the statement provided.

Therefore, the amount increased in $2014$ will be the money spend in $2013$ plus $45.3\%$ of money spent in 2013.

Consider that x billion dollars were spent in 2013.

Therefore, the mathematical model can be represented as mentioned below.

$x+45.3\%\cdot x=16.1$

Take the common factor out and simplify for x.

$\begin{array}{c}x\left(1+\frac{45.3}{100}\right)=16.1\\ x\left(145.3\right)=1610\\ x=\frac{1610}{145.3}\\ =11.08\end{array}$

Hence, the mathematical model is $x+45.3\%\cdot x=16.1$ and the money spent in 2013 was

$\$11.08\text{ billion}$.