X=10
This is the answer to sol e for your equation you are asking
This is the answer to sol e for your equation you are asking
The difference between 9 thirty-sevens and 8 thirty-sevens
2 answers:
You might be interested in
Step-by-step explanation:
So a three digit number can be expressed as: where a is the third digit, b is the second digit, and c is the first digit. Or in other words a is the hundreds place, b is the tens place, and c is the ones place. When something "increases" by 30%, it is 130% it's original value, and to calculate how much that is, you simply convert 130% to a decimal by dividing by 100, which gives you 1.30. And since all the digits are increased by 1, you have the equation:
Distribute the multiplication on the left side:
Distribute the multiplication on the right side:
Add like terms on the left side:
Subtract 100a, 10b, and c from both sides
So "technically" you can just plug in any two values, and then solve for the last value, but since you have a 3 digit number, you have the restriction of a < 10, b < 10, and c < 10, and also a, b, and c, should only be integers and all have the same sign or it wouldn't be a 3 digit number.
So let's start with a, since it has the highest coefficient, well you can fit 30 into 111, 3 times without going over so that's the first value
111 = 30(3) + 3b + 0.3c
111 = 90 + 3b + 0.3c
Now subtract the 90 from both sides
21=3b+0.3c
Well 3 can fit into 21, 7 times!
21 = 3(7) + 0.3c
21 = 21 + 0.3c
subtract 21 from both sides
0 = 0.3c
and now obviously c is 0, if you want you can divide both sides by 0.3 but it's a bit redundant
c = 0
This gives you the three values, a=3, b=7, c=0. which is the number 370. Now let's double check. Adding 1 to each digit would give you 481 and 481/370 = 1.3, so it is correct!
part b:
So to prove there is no three digit number, is to realize there is no solution, given the restriction or integers, greater than or equal to 0, and less than 10, and all of them must have the same sign.
So let's start with the same equation except this time instead of 1.3 it's 1.4
Distribute on the left side;
Distribute on the right side:
Add like terms on left side:
Subtract 100a, 10b, and c from both sides:
Now to do the same process, let's start by finding how many times we can fit 40 into 111, and if you're wondering why we start with 40, it's because let's say for example I just say, I can fit another 40 into it, but I decide not to, and let b do that, well even if it's just 40, b will have be at least 10, which does not fit our restrictions, so you have to fit as many 40's into the number first then go the other numbers.
So only 2 40's can fit in 111 without going over the value
111 = 40(2) + 4b + 0.4c
Subtract 80 from both sides
4 can fit into 31, 7 times
31 = 4(7) + 0.4c
31 = 28 + 0.4c
subtract 28 from both sides
3 = 0.4c
divide both sides by 0.4
7.5 = c.
Since c is not an integer there is no 3 digit number that exists that increases by 40% whenever you increase it by 1.
Answer:
Step-by-step explanation:
This is quite a doozy, my friend. We will set up a d = rt table, fill it in...and pray.
The table will look like this before we even fill anything in:
d = r * t
SUV
sedan
Ok now we start to pick apart the problem. Motion problems are the hardest of all story problems ever. This is because there are about 100 ways a motion problem can be presented. So far what we KNOW for an indisputable fact is that the distance from Georgetown to Greenville is 120 km. So we fill that in, making the table:
d = r * t
SUV 120
sedan 120
The next part is derived from the sentence "After an hour, the SUV was 24 km ahead of the sedan." This tells us the rate of the SUV in terms of the sedan. If the SUV is 24 km ahead of the sedan in 1 hour, that tells us that the rate of the sedan is r and the rate of the SUV is r + 24 km/hr. BUT we have other times in this problem, one of them being 25 minutes. We have a problem here because the times either have to be in hours or minutes, but not both. So we will change that rate to km/min. Doing that:
24 ×
So now we can fill in the rates in the table:
d = r * t
SUV 120 = r + .4
sedan 120 = r
They left at the same time, so now the table looks like this:
d = r * t
SUV 120 = r + .4 * t
sedan 120 = r * t
We will put in the time difference of 25 minutes in just a sec.
If d = rt, then the equation for each row is as follows:
SUV: 120 = (r + .4)t
sedan: 120 = rt
Since the times are the same (because they left at the same time, we will set the equations each equal to t. The distances are the same, too, I know that, but if we set the distances equal to each other and then solve the equations for a variable, the distances cancel each other out, leaving us with nowhere to go. Trust me, I tried that first! Didn't work.
Solving the first equation for time:
sedan: That's the easy one. Now the SUV. This is where that time difference of 25 minutes comes in from the last sentence. Let's think about what that sentence means in terms of the times of each of these vehicles. If the sedan arrived 25 minutes after the SUV, then the sedan was driving 25 minutes longer; conversely, if the sedan arrived 25 minutes after the SUV, then the SUV was driving 25 minutes less than the sedan. The latter explanation is the one I used in the equation. Again, if the SUV was driving 25 minutes less than the sedan, and the equations are solved for time, then the equation for the SUV in terms of time is
and we solve that for t:
Again, going off the fact that times they both leave are the same, we set the equations equal to one another and solve for r:
I began by first multiplying everything through by (r + .4) to get rid of it in the denominator. Doing that:
which simplifies very nicely to
So maybe it's not so nice. Let's keep going:
and keep going some more:
and now we multiply everything through by r to get rid of THAT denominator:
giving us:
Now we have a second degree polynomial we have to solve by factoring. Get everything on one side and factor using the quadratic formula.
That factors to
r = 1.2 and r = -1.6 and both of those rates are in km/minute. First of all, we cannot have a negative rate (this is not physics where we are dealing with velocity which CAN be negative) so we throw out the -1.6 and convert the rate of 1.2 km/minute back to km/hr:
×
and we get
r = 72 km/h, choice B.
Wow...what a pain THAT was, right?!