Your unknown is the number of miles that will make the costs equal for both agencies. x is the number of miles. For the first agency, c1, we will represent the cost per mile as .15x. No matter how many miles you drive you will be paying a 25 dollar fee. The equation for this agency is c1(x) = .15x + 25. c2 is the other agency that charges .21 cents per mile which is expressed as .21x, and no matter how many miles you drive with that rental you are paying 18 dollars a day. That equation is c2(x) = .21x + 18. Now, the problem asks us, "...for what number of miles will the two plans be equal?" That means that it wants us to set those 2 equations we just wrote equal to each other and solve for x. .15x + 25 = .21x + 18. .06x = 7 and x=116.7. That means no matter what agency you pick to rent from, the cost at both will be the same when you have driven 116.7 miles. After that, one will be cheaper again (you could graph those lines to find out which one!), but at 116.7 miles exactly the rentals cost the same.
Step-by-step explanation:
x = number of true/false questions
y = number of multiple choice questions
x + y = 40
2x + 3y = 144
from the first equation we get
x = -y + 40
this identity we can then use in the second equation
2(-y + 40) + 3y = 144
-2y + 80 + 3y = 144
y + 80 = 144
y = 64
and
x + 64 = 40
x = -24
that does not make any sense.
something is wrong with the problem description.
just think about it :
40 questions - if all of them would be multiple choice tests (creating the max. possible points for 40 questions), we could have only 40×3 = 120 points.
but the description says 144 points.
for 144 points we need at least 48 (144/3) questions.
that does not fit.
the described system does not have any natural number solution. therefore we are getting such crazy numbers as result, when we try.
Yes, the answer to the system is infinitely many solutions as the solution 17=17 is reflexive.