Certainly! Let's break down the problem and solve for the number of bars per person, denoted as [tex]\( a \)[/tex].
We start with the given equation:
[tex]\[ x = \frac{y \cdot z}{a} \][/tex]
where:
- [tex]\( x \)[/tex] is the number of people at the event,
- [tex]\( y \)[/tex] is the number of ice-cream bars per box,
- [tex]\( z \)[/tex] is the number of boxes,
- [tex]\( a \)[/tex] is the number of bars per person.
We need to isolate [tex]\( a \)[/tex] on one side of the equation to solve for it. Here are the steps to do that:
1. Multiply both sides of the equation by [tex]\( a \)[/tex] to eliminate the denominator on the right side:
[tex]\[ x \cdot a = y \cdot z \][/tex]
2. Next, divide both sides by [tex]\( x \)[/tex] to isolate [tex]\( a \)[/tex]:
[tex]\[ a = \frac{y \cdot z}{x} \][/tex]
So, the number of ice-cream bars available for each person, [tex]\( a \)[/tex], is given by:
[tex]\[ a = \frac{y \cdot z}{x} \][/tex]
Therefore, the formula to determine the number of bars per person is:
[tex]\[ \boxed{a = \frac{y \cdot z}{x}} \][/tex]
This tells us that to find out how many ice-cream bars each person will get, you simply multiply the number of bars per box by the number of boxes and then divide by the number of people.
