Pl explain step by step and in linear equation with single variable form , the following problems,?

Question

1)A number is divided into 2 parts such that one is 10 more than the other. if the 2 parts are in the ratio 5:3, find the number.


2)if 1/2 is substracted from a number and the difference is multiplied by 4 the result is 5, find the number.


3)Jane and Jean start walking from the same place in opposite directions. If Jane walks at a speed of 2 and 1/2 km per hourand Jean at 2 km /per hour, in how much time will they be 18 km apart?

Answer 1

1)A number is divided into 2 parts such that one is 10 more than the other. if the 2 parts are in the ratio 5:3, find the number.

Let the smaller part be n. Therefore the other part is n + 10
(n + 10)/n = 5/3
Multiply by n
n + 10 = 5n/3
Multiply by 3
3(n + 10) = 5n
Therefore 3n + 30 = 5n
Take 3n from both sides
30 = 2n
So n = 15 and n + 10 = 25
So the original number was 15 + 25 = 40

2)if 1/2 is substracted from a number and the difference is multiplied by 4 the result is 5, find the number.
Let the number be n
Thus the difference = n - 1/2
4(n - 1/2) = 5
So 4n - 2 = 5
Add 5 to both sides
4n = 7
n = 7/4
= 1 3/4

3)Jane and Jean start walking from the same place in opposite directions. If Jane walks at a speed of 2 and 1/2 km per hourand Jean at 2 km /per hour, in how much time will they be 18 km apart?

Let them walk for t hours
In this time Jane walks 2 1/2 t km ie 5t/2 km
and Jean walks 2t km
So they are (2t + 5t/2) km apart

So 2t + 5t/2 = 18
Multiply everything by 2
4t + 5t = 36
ie 9t = 36
So t = 4
ie it takes 4 hours for them to be 18 km apart

Answer 2

Hi Scarlett!

Here we go:

1) Here, you have two numbers y and x, so that

y = x + 10
y = (5/3)*x

So

x + 10 = (5/3)*x
3*(x+10) = 5*x
3*x + 30 = 5*x
3*x - 5*x +30 = 0
-2*x = -30
2*x = 30
x = 15

Since y = x+10, then y = 25 and your number is a z=x+y=15+25, which turns out to be 40 (the number I suppose you need to find).

2) Here you have a number (x) from which you take out 1/2 and multiply the difference by 4. This is a bit easier.

4*(x - 1/2) = 5
4*x - 2 = 5
4*x = 7
x = 7/4 (your number)

3) The equation they should follow is s=v*t, where s is the distance, v is the speed and t is the time. So:

S(Jane) = 2.5*t
S(Jean) = 2*t

The distance between them should be 18km, and they are walking in opposite directions. So,

S(Jane) - S(Jean) = 18
2.5*t - 2*t = 18
0.5*t = 18
t = 18*2

t = 36 hours.

Answer 3

1) Let's call the smaller part A and the larger part B. The two pieces of information you have about A and B can be written algebraically as

B = A+10

and

5A = 3B.

Now, if we multiply the first equation by 3 we get:

3B = 3A + 30

and then using the second equation we can substitute the 3B by 5A and get:

5A = 3A + 30

or, rearranging:

2A = 30, or A=15.

From the first equation we then work out that B=25. So the total number of which A and B are the two parts is 40.

How's that? Can you do the others now?

Answer 4

1)

say two parts are x and y (the number is x+y)

so x = y+10 - (i)

and x/y=5/3 - (ii)

from (ii) we get,

x = 5/3y

putting this value to (i), we get

5/3y = y+10
or, 5y = 3y+30
or, 2y = 30
or, y =15

now putting this value in (i) we get

x = 15+10 = 25

So the number is (25+15) or 40 .. cool :)

2)
say the number is m

from given conditions we get,
so 4(m - 1/2)=5
or, 4m -2=5
or, 4m =7
or m =7/4

(I think the result should have been 6 instead of 5... to make the missing no 8.. anyway..)

3)
Jane a Jean makes a difference between themselves 4.5 km in every hour

Thus to make 18 km difference /distance between them they will need 18/4.5 hours = 4 hours

cool :)

Answer 5

1.let the numbers be 3x and 5x
5x-3x=10
2x=10
dividing by 2
x=5
the nos are(3x)15and(5x) 25 respectively

2.(x-1/2)*4=5
4x-2=5
adding 2
4x=7
dividibg by 4
x=7/4
=1 3/4

3.since they are walking in opposite directions the relative speeds will get added up
relative speed =4 1/2 kmph
distance aparet=18 km
time=distance/speed
=18/(4 1/2)
=18/(9/2)
18*2/9
=4 hrs

Answer 6

continually combine "like words" combine words like " 7 and 18 like "5x and 2x" in this venture: 7 - 5x = 17 we combine "7 and 17" 7 - 5x = 17 - 5x = 17 - 7 - 5x = 10 - 5x/-5 = 10/ -5 x = -2