Question

The distance from Kim's house to NYC is 100 miles more than the distance from her house to LA. If the sum of the distances is 3,000 miles, how far is it from Kim's house to NYC?

Answer 1

The distance from Kim's house to NYC is 1,550 miles.

Step-by-step explanation:

Let's set up the problem with variables. Let the distance from Kim's house to NYC be x miles, and let the distance from Kim's house to LA be y miles. We are told that x = y + 100.

Since the sum of the distances is 3,000 miles, we can write the equation x + y = 3,000.

Now we can solve the system of equations:

x = y + 100

x + y = 3,000

Substitute the value of x from the first equation into the second equation:

(y + 100) + y = 3,000

Combine like terms: 2y + 100 = 3,000

Subtract 100 from both sides: 2y = 2,900

Divide by 2: y = 1,450

Now substitute the value of y back into the first equation to find x:

x = 1,450 + 100 = 1,550

Therefore, the distance from Kim's house to NYC is 1,550 miles.

Answer 2

Distance from kims house to NYC is 1550 miles

Solution:

Let "a" be the distance from kims house to NYC

Let "b" be the distance from kims house to LA

Given that distance from Kim's house to NYC is 100 miles more than the distance from her house to LA

Therefore,

distance from Kim's house to NYC = 100 + distance from her house to LA

a = 100 + b ------ eqn 1

The sum of the distances is 3,000 miles

distance from kims house to NYC + distance from kims house to LA = 3000

a + b = 3000 ------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

100 + b + b = 3000

2b = 3000 - 100

2b = 2900

b = 1450

From eqn 1,

a = 100 + 1450

a = 1550

Thus distance from kims house to NYC is 1550 miles