Chapter 1.3, Problem 19Q

a.

To determine

To write and solve the equation according to the given situation

Answer to Problem 19Q

3 hours

Explanation of Solution

Given:

  

Formula Used:Total Amount to be paid = Price of vase + Studio fee × Hours painted

Calculation:

Let, the painted hours when the amount to be paid for both studios become equal be x hours.

  

From the above figure:

Amount to be paid for Studio A for x hours of painting = $(10 + 8x )

Amount to be paid for Studio B for x hours of painting = $(16 + 6x )

For the calculation of time when same amount was paid:

  $\begin{array}{l}\Rightarrow 10+8x=16+6x\\ \Rightarrow 8x-6x=16-10\\ \Rightarrow 2x=6\\ \Rightarrow x=3\end{array}$

Conclusion:

Therefore, in 3 hours of painting the total amount paid will be equal.

b.

To determine

To write and solve the equation according to the given situation

Answer to Problem 19Q

3 hours.

Explanation of Solution

Given:

  

Formula Used:Total Amount to be paid = Price of vase + Studio fee × Hours painted

Calculation:

Let, the painted hours when the amount to be paid for both studios become equal be x hours.

  

But, now studio B increases the hourly charges by $2, which means the hourly charges for studio B becomes $8 and rest of the data remain the same as earlier case

From the above figure and change in data as the question:

Amount to be paid for Studio A for x hours of painting = $(10 + 8x )

Amount to be paid for Studio B for x hours of painting = $(16 + 8x )

For the calculation of time when same amount was paid:

  $\begin{array}{l}\Rightarrow 10+8x=16+8x\\ \Rightarrow 10=16\end{array}$

The above result obtained is mathematically incorrect.

This means that the assumption of both the prices to be same will never be true if the hourly charges of Studio B are increased by $2.

Conclusion:

Therefore, the prices of both the studios will never be equal in this case contrary to the previous case.