The height of Seven falls in Colorado is 5 over 2 the height in feet of Twin Falls in Idaho the sum of the heights is 420 ft find the height of each?

Answer 1

What we're going to do is find out the height of Twin Falls.

We know that Seven Falls (x) is 5/2 as much as Twin Falls. So, bearing that in mind, we turn it into an equation which reads as:

x + 5/2x = 420

(Twin Falls plus 5/2 the amount of Twin Falls equals Four Hundred Twenty.)

We must combine like-variables. But with the fraction involved, first find the common denominator and multiply it by all sides. In this circumstance, the denominator is two.

2(x + 5/2x) = 2(420)

(Distributive property is simpler and quicker.)

2x + 5x = 840

(After multiplying 5/2 by 2/1. The twos cancel each other out, leaving us with 5/1.)

Combine like variables.

7x = 840

Divide both sides by seven, leaving us with:

x= 120

120ft is the height for Twin Falls. Now we must find the height for Seven Falls, which is 5/2 times more than Twin Falls.

120/1 x 5/2 = 300/1

(By cross-multiplying, we determine that two goes into 120 sixty times. Sixty times 5 is 300.)

So we have the height for both Twin Falls(120ft) and Seven Falls(300ft).

Check:

The sum of the heights is 420ft.

120 + 300 = 420.