Chapter 8.10, Problem 31STP

To determine

The correct option which represent the number of pictures taken by each person when the Jennifer has 16 times lesser than Amy and Amy has taken the three times pictures as Jennifer.

F. Amy took $8$ pictures and Jennifer took $24$ pictures.

G. Amy took $24$ pictures and Jennifer took $8$ pictures.

H. Amy took $16$ pictures and Jennifer took $6$ pictures.

J. Amy took $6$ pictures and Jennifer took $16$ pictures.

Answer to Problem 31STP

The correct option is G. Amy took $24$ pictures and Jennifer took $8$ pictures.

Explanation of Solution

Given:

The given equations are as:

  $\begin{array}{l}a=3j\\ a=j+16\end{array}$

Where,

Amy: $a$

Jennifer: $j$

Calculation:

Now, the given condition written in the form eqn:

  $a=3j$....... (1)

  $a=j+16$....... (2)

Put the value of $a=3j$ in eq. (2):

  $\begin{array}{l}a=j+16\\ 3j=j+16\\ 2j=16\\ j=8\end{array}$

Now, the value of $a$ is calculated as:

  $a=3j=3\times 8=24$

That means, Amy took $24$ pictures and Jennifer took $8$ pictures.

Conclusion:

Hence, the correct option is G.