5(x - 1) and 5x - 1is it equivalent
2 answers:
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<u>Corrected Question</u>
Ping lives at the corner of 3rd Street and 6th Avenue. Ari lives at the corner of 21st Street and 18th Avenue. There is a gym 2/3 the distance from Ping's home to Ari's home. Where is the gym?
- 9th Street and 10th Avenue
- 12th Street and 12th Avenue
- 14th Street and 12th Avenue
- 15th Street and 14th Avenue
Answer:
(D)15th Street and 14th Avenue
Step-by-step explanation:
Ping's Location: (3rd Street, 6th Avenue)
Ari's Location: (21st Street, 18th Avenue)
The gym is at point P which is the distance from Ping's home to Ari's home.
That is, Point P divides the line segment in the ratio 2:1.
We use the section formula:
m:n=2:1,
The gym is located at 15th Street and 14th Avenue.
Given the set of equations:
2x + y = 10
y = 3x
Let's solve for x and y.
Here, let's use substitution method.
Substitute 3x for y in equation 1:
2x + y = 10
2x + 3x = 10
5x = 10
Divide both sides by 5:
In equation 2, substitute 2 for x to find y.
y = 3x
y = 3(2)
y = 6
Therefore, we have:
x = 2 and y = 6
ANSWER:
x = 2, y = 6