Sure! Let's break it down step by step to find out how many z's are there when 12x is given.
1. Start with the given equations:
- Equation 1: 8x = 5y
- Equation 2: 3y = 14z
2. We need to eliminate one variable to solve for the other variables. Let's start by solving Equation 2 for y:
- Divide both sides of Equation 2 by 3: (3y) / 3 = (14z) / 3
- Simplifying, we get: y = (14z) / 3
3. Now, substitute the value of y from Equation 2 into Equation 1:
- Replace y in Equation 1 with (14z) / 3: 8x = 5 * ((14z) / 3)
- Simplifying further, we get: 8x = (70z) / 3
4. We want to find the value of 12x. So, multiply both sides of the equation by 12:
- Multiply both sides of the equation by 12: 12 * 8x = 12 * ((70z) / 3)
- Simplifying, we get: 96x = (840z) / 3
5. Further simplification:
- Multiply both sides of the equation by 3: 3 * 96x = 3 * ((840z) / 3)
- Simplifying, we get: 288x = 840z
6. Finally, we have the equation 288x = 840z. Now, let's find how many z's are there when 12x is given:
- Divide both sides of the equation by 288: (288x) / 288 = (840z) / 288
- Simplifying, we get: x = (840z) / 288
So, when 12x is given, it is equivalent to (840z) / 288, which means there are (840z) / 288 z's.