2 buildings have 60 floors altogether. Building A has 3 floors for every 2 floors of building B. How many floors does each building have?
A+B = 60 (1)
A/3 = B/2
A = 3B/2 (2)
combine (1) and (2)
3B/2+B = 60
3B/2+2B/2 = 60
5B/2 = 60
B = 24
A = 36
Let's solve this problem step by step.
First, let's assign variables to the number of floors in building A and building B.
Let's say the number of floors in building A is "x" and the number of floors in building B is "y".
According to the problem, the total number of floors in both buildings is 60. So, we can write the equation:
x + y = 60 ...(Equation 1)
We are also given that the ratio of the number of floors in building A to building B is 3:2, or 3/2.
This means that for every 3 floors in building A, there are 2 floors in building B. Mathematically, we can write:
x/y = 3/2 ...(Equation 2)
To solve these equations, we can use a method called substitution.
Rearranging Equation 2, we can write it as:
x = (3/2)y
Now, substitute this value of x in Equation 1:
(3/2)y + y = 60
Combine like terms:
(5/2)y = 60
To isolate y, we multiply both sides of the equation by 2/5:
y = (60 * 2/5)
y = 24
Now, substitute the value of y back into Equation 1 to find x:
x + 24 = 60
x = 60 - 24
x = 36
Therefore, building A has 36 floors and building B has 24 floors.