Question

Katy is between Houston and San Antonio. If the distance from Katy to San Antonio is 2 x x  5 miles and the distance from Katy to Houston is 4 12 x  miles. The total distance from Houston to San Antonio is 120 miles . Then How far is it between each City?

Answer 1

It is hard to read what you actually wrote, but i guess this is:

Distance to San Antonio = 2*5*x mi

Distance to Houston = 4*12*x mi

Distance from Houston to San Antonio = 120mi

Then we must have that:

2*5*x mi + 4*12*x mi = 120mi

(2*5 + 4*12)*x mi = 120mi

(10 + 48)*x mi = 120mi

x mi =120/58 mi = 2.06 mi

Now we can replace it in the above equations:

Distance to San Antonio = 2*5*2.06 mi = 20.6 mi

Distance to Houston = 4*12*2.06 mi = 98.88 mi