The distance from Jim's house to the intersection of Thornwood Drive and Holly Drive is given by the expression 15x − 7. The total distance from Jim's house to Adam's house when traveled on Thornwood Drive and Holly Drive is given by the expression 23x − 2. Find a single expression that represents the distance from Adam's house to the intersection of Thornwood Drive and Holly Drive.
A) 8x + 5
B) 8x − 9
C) 38x + 5
D) 38x − 9
Can someone help me on this one I am puzzled, can they guide me through how to do it?
Draw a map. It should be clear that you want
(23x-2) - (15x-7)
To find the distance from Adam's house to the intersection of Thornwood Drive and Holly Drive, we need to subtract the distance from Jim's house to the intersection from the total distance from Jim's house to Adam's house.
Let's call the distance from Jim's house to the intersection "d1" and the total distance from Jim's house to Adam's house "d2".
Given:
d1 = 15x - 7
d2 = 23x - 2
To find the distance from Adam's house to the intersection, we subtract d1 from d2:
Distance from Adam's house to the intersection = d2 - d1
= (23x - 2) - (15x - 7)
= 23x - 2 - 15x + 7
= (23x - 15x) + (7 - 2)
= 8x + 5
Therefore, the single expression that represents the distance from Adam's house to the intersection of Thornwood Drive and Holly Drive is:
A) 8x + 5
To find the distance from Adam's house to the intersection of Thornwood Drive and Holly Drive, we need to subtract the distance from Jim's house to the intersection from the total distance from Jim's house to Adam's house.
Let's call the distance from Adam's house to the intersection of Thornwood Drive and Holly Drive "y". We know that the distance from Jim's house to the intersection of Thornwood Drive and Holly Drive is given by 15x - 7, and the total distance from Jim's house to Adam's house on Thornwood Drive and Holly Drive is given by 23x - 2.
So, the distance from Adam's house to the intersection can be calculated as (23x - 2) - (15x - 7).
Simplifying the expression, we have:
(23x - 2) - (15x - 7) = 23x - 2 - 15x + 7
Combining like terms, we get:
23x - 15x - 2 + 7 = 8x + 5
Therefore, the single expression that represents the distance from Adam's house to the intersection of Thornwood Drive and Holly Drive is 8x + 5.
Hence, the correct answer is A) 8x + 5.