The Washington Monument is 555 feet tall. It is 75 feet shorter than the Gateway to the West Arch.

Question

Objective: Write equations and equalities.

Please Help

Answer 1

In word problems "is"  tends to mean is equal to or "=". When talking about heights taller would be greater than ">" and shorter would be less than "<".

 

For example:

The building is 10 feet tall would translate to:

building height = 10feet

 

The building is taller than the person would become:

building height> person height

 

The building is shorter than the sky scraper would be:

building height< skyscraper height

 

You could also combine the  previously given  information to find:

skyscraper height > building height =10 feet > person height

 

In the word problem you presented, you are told " the Washington Monument is 555 feet tall"  this means

Washington Monument height = 555 feet

 

you are also told it is 75 feet shorter than the Gateway to the West Arch

this sentence can be separated into two equation/ inequalities.

First, the Washington monument is shorter than the Gateway to the West Arch or

 

Washington Monument height<Gateway to the West Arch height

 

Second, the Washington Monument is 75 feet shorter than the Gateway to the West Arch or

Washington Monument height= Gateway to the West Arch height - 75 feet

you subtract 75 feet from the height of the Gateway to the West Arch because it has already been determined that Washington Monument height<Gateway to the West Arch height

If you are trying to solve for the height of the Gateway to the West Arch you can do so by plugging in the the Washington Monument height (555 feet) into the last equation and adding 75 feet to each side.

555 feet =Gateway to the West Arch height - 75 feet

555 feet+ 75 feet =Gateway to the West Arch height - 75 feet +75 feet

630 feet=Gateway to the West Arch height +0

630 feet=Gateway to the West Arch height

 

Hope this helps.

Answer 2

Let W = height of Washington Monument

Let G = height of Gateway to the West Arch

 

W = 555 ft

G =  W + 75 ft   (because the Washington Monument is 75 ft shorter than Gateway Arch)

 

G = 555 + 75 = 630 ft

 

We are given exact height in the problem, so there are no inequalities

involved as the problem is written.  If the problem had stated that the

Gateway Arch is "at least" 75 ft taller (which would be silly since it is

a single fixed height) then we could have set up an inequality.