i need mathematician: help me solve this math problem..?

Question

a) for two consecutive whole numbers, the sum of the smaller and twice the larger is 38. Find the numbers.

b) the sum of two numbers is 34. four times the smaller number is 4 less than the larger number. what are the numbers?

c) a lion's top speed is twice the top speed of an elephant. the sum of the top speeds is 120km/h. Find the top speed of each animal.

Answer 1

a) Let the first number be x then the second number consecutive to it will be x + 1
so,
x + 2 (x+1) = 38
x + 2x + 2 = 38
3x = 36
x = 12
x+1 = 13

b) let the two numbers be x and y and let y be the larger number
x + y = 34
y = 34 - x

but 4x = y - 4
substitute y = 34-x in the above to get;
4x = 34-x -4
4x + x = 34 - 4
5x = 30
x = 6
y = 34 - 6 = 28
the numbers are 6, 28

c) Let lions's speed be x
let elephant's speed be y
x = 2y (Lion's speed is twice elephant's speed)

x + y = 120 (sum of speeds is 120)
subsitute x = 2y in the above to get
2y + y = 120
3y = 120
y = 120/3 = 40 Km/h (Elephant's Speed)
x = 2y = 2 * 40 = 80 Km/h (Lion's Speed)



so the numbers are 12, 13

Answer 2

a) Let n be the smaller of the two numbers. Then the other is n+1, since they're consecutive. We're told n + (n+1) = 38. Solve this for n.

b) Let A and B be the two numbers. We're told A+B=34 and 4A = B - 4. You have two equations with two unknowns, so solve for A and B using substitution.

c) Let L be the lion's speed and E the elephant's. Then L = 2E, and L+E = 120. Again, use subsitution to solve.

Answer 3

a) Let x be the smaller number and x+1 be the larger number

x + 2(x+1) = 38
3x = 36
x=12
x+1 = 13

The numbers are 12 and 13.

b) Let x be the smaller number and 4x + 4 be the larger number as derived from the problem

x + 4x + 4 = 34
5x = 30
x=6
4x+4 = 28

The numbers are 6 and 28.

c) Let x be the elephant's top speed and 2e be the lion's top speed

e + 2e = 120
3e=120
e=40
2e=80

Lion's speed 80kph
Elephant's speed 40 kph

Answer 4

a) 2 consecutive nos: x, x+1
x + [2(x+1)] = 38
x + 2x + 2 =38
3x + 2 =38
3x =36
x =12 x+1=13


b) x+y=34 , x=34-y
4x=y-4
substitute x=34-y to 4x=y-4
4(34-y)=y-4
136-4y=y-4
140 =5y
y =28
x =34-y
=34-28
x =6

c) L = 2E
L+E=120
substitute L=2E to L+E=120
2E + E =120
3E =120
E = 40 km/hr, elephant's top speed
L = 2E
=2(40)
L =80 km/hr, lion's top speed

Answer 5

a)let the numbers be x and y
y= x+1
x+2y=38
but y=x+1
therefore 2(x+1)+x=38
3x=36
x=12 and y=13
the numbers are 12 and 13

b) let the numbers be y and x
y+x =34
let x be the smaller number,
4x= y-4
but y=34-x
4x=34-x-4
5x=30
x=6 and y=28
the numbers are 6 and 8

c)let the lions speed =l and the elephants=e
1=2e
but e+2e=120
3e=120
e=40 and l=80
therefore the top speed of a lion is 80km/h and that of an elephant is 40km/h

Answer 6

A)
x+ 2(x+1)=38
x+2x+2=38
3x+2=38
3x=36
x=12
{12, 13}


B)
s+L=34
4s=L-4
4s=(34-s)-4
4s=30-s
5s=30
s=6, L=28

C)
L=2E
L+E=120
2E+E=120
3E=120
E=40, L=80

Answer 7

I would say it really depends at what level you are talking about. Yes I would say quite a bit of honest to god research mathematics are conducted with computers. However if you look at alot of the college level math going on I would say it is about 50/50. Mathematics and computer programming crosses over in so many fields that is becoming almost the same thing with just different focuses. Combinitorics, statistics, and Topology are some of the math fields that computer use is pretty much a given. (Topology it is more of a usefull tool in making presentations). Other classes like Abstract Algebra, Group theory, and most of your Calculus courses are more of a pen and paper type of math although computers can be helpfull in those as well. In general I would say that most of use use the pen and paper method when we are going to be doing alot of manipulation with the equations and want to be able to see step by step what we will be doing. I happen to believe that in many cases writing it all out can be faster... And there is no doubt in my mind that it helps you learn the material better. There is a certain connectiveness to accually writing out alot of your work rather than plugging it in to a computer and watch it crank out the answer.

Answer 8

a= 12 &13
b=6&28
c= lion 80 &elephant 40

Answer 9

a) x+2(x+1)=38
x+2x+2=38
3x=36
x=12: The numbers are 12 and 13.

b) a+b=34
4a=b-4
b=4a+4
a+4a+4=34
5a=30
a=6:
b=34-6=28
a=6 and b=28

c) L=2E
L+E=120
2E+E=120
3E=120
E=40
L=80

The elephant is 40 km/h and the lion is 80 km/h.

Answer 10

a) 12 and 13

b) 28 and 6

c) lion = 80 km/h
elephant = 40 km/h