If 5x's = 4 y's and 12 y's = 5 z's, then 30x's = how many z's?
y=5/12 x
x=4/5 y=4/5 * 5/12 z reduce it
= z/3
30x=10z
To solve this problem, we need to use the given equations to find the relationship between x's and z's. Let's start by finding the relationship between x's and y's.
We are given that 5x's = 4y's. This means that for every 5 x's, there are 4 y's. To find the relationship between y's and z's, we are given that 12 y's = 5 z's. So, for every 12 y's, there are 5 z's.
Now, we can use these two relationships to find the relationship between x's and z's. Let's start by finding the relationship between x's and y's, and then between y's and z's:
5x's = 4y's
12y's = 5z's
To find the relationship between x's and z's, we can combine these two equations. Let's solve for y's in the first equation by dividing both sides by 4:
(5x's)/4 = y's
Now, substitute this expression for y's in the second equation:
12[(5x's)/4] = 5z's
Simplifying this equation, we get:
60x's/4 = 5z's
15x's = 5z's
Now, we have the relationship between x's and z's. For every 15 x's, there are 5 z's. To find how many z's there are in 30 x's, we can set up a proportion:
15x's = 5z's
30x's = ?z's
We can cross-multiply and solve for ?z's:
(30x's)(5) = ?z's
150x's = ?z's
So, 30x's is equal to 150 z's.