steve can you explain step by step please
8x=5y and 3y=14z then 12x= how many z's
you know that 8x = 5y
you know that 3y=14z
since 5 = (5/3)*3, 5y = (5/3)*(3y) so,
5y = (5/3)(3y) = (5/3)(14z) = (70/3)z
now you have 5y, which is the same as 8x. You want 12x.
since 12 = (3/2)*8, 12x = (3/2)*8x.
12x = (3/2)(8x) = (3/2)(5y) = (3/2)(70/3)z = (70/2)z = 35z
Don't know how I can clear it up any more.
3 y = 14 z
so
y = (14/3) z
8 x = 5 (14/3) z
x = (5/8)(14/3)z
12 x = 12(5/8)(14/3)z = 35 z
Hi Steve
When you have time can you please step in how did you resolve this problem?
Reason to follow up is how did you get 2's and 3's
Thx
K
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.