# Florida's coastline is 118 miles shorter than four times the coastline of Texas. It is also 983 miles longer than the coastline of Texas. What are the lengths of the coastlines of Florida and Texas?

Mar 26, 2018

Coastline of Florida is $1271.3 \overline{3} \setminus \setminus \setminus$ miles.

Coastline of Texas is $288.3 \overline{3} \setminus \setminus \setminus \setminus \setminus \setminus \setminus$ miles.

#### Explanation:

Let $F$ be Florida's coastline and $T$ be Texas' coastline:

Florida's coastline is 118 miles shorter than four times the coastline of Texas. We can express this as follows:

$F - 118 = 4 T$

Florida's coastline is 983 miles longer than the coastline of Texas.

$F = T + 983$

We now solve these equations simultaneously:

Substituting $F = T + 983$ into $F - 118 = 4 T$:

$T + 983 - 118 = 4 T$

$T + 865 = 4 T$

Subtract T from both sides:

$3 T = 865$

Divide by 3:

$T = \frac{865}{3} = 288.3 \overline{3}$

Substituting this in $F = T + 983$

$F = \frac{865}{3} + 983$

$F = \frac{3814}{3} = 1271.3 \overline{3}$

Coastline of Florida is $1271.3 \overline{3} \setminus \setminus \setminus$ miles.

Coastline of Texas is $288.3 \overline{3} \setminus \setminus \setminus \setminus \setminus \setminus \setminus$ miles.