To find the unknown quantity in the percent problem, we use the formula [tex]\( R \cdot B = A \)[/tex], where [tex]\( R \)[/tex] is the rate, [tex]\( B \)[/tex] is the base or unknown quantity we are trying to find, and [tex]\( A \)[/tex] is the amount.
Here is the step-by-step solution:
1. Convert the Percentage to a Decimal:
The rate [tex]\( R \)[/tex] is given as 142%. To convert a percentage to a decimal, divide by 100:
[tex]\[
R = \frac{142}{100} = 1.42
\][/tex]
2. Set Up the Equation:
We know [tex]\( R \cdot B = A \)[/tex]. The amount [tex]\( A \)[/tex] is given as 690. Substituting the values we have:
[tex]\[
1.42 \cdot B = 690
\][/tex]
3. Solve for [tex]\( B \)[/tex]:
To find [tex]\( B \)[/tex], divide both sides of the equation by 1.42:
[tex]\[
B = \frac{690}{1.42}
\][/tex]
4. Calculate the Value:
Performing the division gives:
[tex]\[
B \approx 485.92
\][/tex]
5. Round to Two Decimal Places:
The result is already rounded to two decimal places. Therefore, the final answer is:
[tex]\[
B \approx 485.92
\][/tex]
So, the unknown quantity is 485.92.
