Answer:
12 bottles were sold in the second hour.
Step-by-step explanation:
This problem can be solved by implementing an equation in one variable.
The equation will utilize the given values including total bottles of juice, the amount of juice sold in the first hour and amount of juice remaining at the end.
The equation will also consist of the value to be found out, the amount of juice sold in the second hour.
The value to be found out is substituted by a variable.
The equation is then solved by transfer of values and/or variable on the opposite side of the equal sign.
When a value/ variable is transferred on the opposite side of the equal sign, the sign of the value/ variable becomes the opposite.
The negative sign becomes positive and multiplication becomes division, and vice-versa.
1. In the first hour, \frac{3}{15} of all the juice was sold.
\frac{3}{15} of 30 is calculated as
\frac{3}{15} x 30 = 6
6 bottles are sold in the first hour.
2. At the beginning of the second hour, the amount of juice remaining is assumed to be a.
3. As per the question, at the end of second hour, the remaining juice is \frac{6}{15}.
\frac{6}{15} of 30 is calculated as
\frac{6}{15} x 30 = 12
12 bottles are remaining at the end of the second hour.
4. Alternatively, at the end of second hour, 30 - 6 - a of the juice is remaining.
We get, 24 - a bottles are remaining at the end of the second hour.
We equate the above expression with 12, we get the following equation.
24 - a = 12
Next, we transfer a from left side to the right side of the equation.
24 = 12 + a
Next, we transfer 12 from right side to the left side of the equation.
24 - 12 = a
=> 12 = a
OR
a = 12
Hence, 12 bottles were sold in the second hour.
