The height of the flagpole is three fourths the height of the school. The difference in their heights is 4.5 m. What's the height of the school? Choices for school's height: 18, 20, 24. Please show work
h = the height of the flagpole
s = the height of the school
h = ( 3 / 4 ) s
s - h = 4.5 m
s - ( 3 / 4 ) s = 4.5
( 1 / 4 ) s = 4.5 Multiply both sides by 4
s = 18
The height of the school = 18 m
Let's assume the height of the school is x meters.
According to the given information, the height of the flagpole is three fourths (3/4) the height of the school. This means the height of the flagpole is (3/4) * x = 3x/4.
The difference in their heights is given to be 4.5 m, so we can set up the equation:
x - (3x/4) = 4.5
To simplify this equation, we can multiply both sides by 4 to remove the fraction:
4(x) - 4(3x/4) = 4(4.5)
4x - 3x = 18
x = 18
Therefore, the height of the school is 18 meters.
To find the height of the school, we can set up a system of equations. Let's denote the height of the flagpole as F and the height of the school as S.
According to the information given, we know that the height of the flagpole is three-fourths the height of the school, so we can write the equation:
F = (3/4)S
We are also told that the difference in their heights is 4.5 meters, so another equation can be written as:
S - F = 4.5
Now, let's solve the system of equations using substitution:
Substitute the value of F from the first equation into the second equation:
S - (3/4)S = 4.5
Multiply through by 4 to remove the fraction:
4S - 3S = 18
Simplify:
S = 18
Therefore, the height of the school is 18 meters.
So, the correct choice for the school's height is 18 meters.