Let x be the number of months.
The first plan is 15 dollars sign up fee and 38 dollars per month. So the equation is 38x + 15.
The second plan is 78 dollars as sign up fee and 31 dollars per month. So the equation is 31x + 78.
We need find when x has the same value in both equations, so we do their equality:
38x + 15 = 31x + 78
Let's subtract 15 from both sides
38x + 15 = 31x + 78
38x + 15 - 15 = 31x + 78 - 15
38x = 31x + 63
Now let's subtract 31x from both sides to have the variables on a side and the numbers on side:
38x = 31x + 63
38x - 31x = 31x - 31x + 63
7x = 63
Divide both sides by 7 to have the variable x on a side and its value on the other:
(7x)/7 = 63/7
x = 9
So at month 9, the 2 plans will cost the same.
Let's check our answers, and let y be the cost:
y = 38x + 15 = 38*9 + 15 = 357
y = 31x + 78 = 31*9 + 78 = 357
Our answer has been approved.
Hope this helps! :D
Answer:
23.52 miles
Step-by-step explanation:
Let us find the number of miles that they would have run.
Kana starts at 9:35 a.m. and runs at an average rate of 7 mph.
Let the time she has spent so far be t.
Speed is given as:
s = d / t
where d = distance and t = time
=> d = s * t
Therefore, for Kana:
d = 7 * t = 7t _____________(1)
Ji-Hun starts at 10:00 am (25 minutes after Hannah) and runs at an average rate of 8 mph.
25 minutes = 25/60 hour = 0.42 hour
So, his time (compared to Kana's) is t - 0.42.
therefore, for Ji-Hun:
d = 8 * (t - 0.42)
=> d = 8t - 3.36 ____________(2)
Equating (1) and (2):
7t = 8t - 3.36
=> 8t - 7t = 3.36
t = 3.36 hours
Therefore, let us find d:
d = 7 * 3.36 = 23.52 miles
So, Ji-Hun will catch up to Kana after 23.52 miles.
Supplementary angles always equal 180. Then you just solve from there.
7x+5x+24=180
12x+24=180
-24 -24
12x=156
/12 /12
X=12
