Math Equation & Inequalities here need help pls! Can u solve this??

Question

Pls include the solution so i can study how to solve tnx!
1. The sum of two no. is 103. The Larger no. is 1 more than five times the smaller number. Find the no.

2. Find a number such that one half of the number is three less than two thirds of that number.

3. The Product of five & the sum of a number & 8 is ten less than thirty times a number

4. When a no. is multiplied by 6, & the product is decreased by 5, the result is 31. find the no.

5. an Integer added to the quotient of the same integer & 4 is equal to 6 more than twice the integer. find the integer...

thats all pls! im goin in a meeting so. pls i need ur help ill go now!

hey guys tnx for ur help! I Just arrived this time! I havent slept yesterday to now! i need rest thank you! you saved my time!

Answer 1

The best way to solve these problems is to set up the equations by translating the sentences into math symbols....
1. look for the verb is or the phrase "is equal" or "the result is" these all translate as the =

2. key words such as more ---> +
less than -----> - sum ----> +
decreased ----> - product ----> multiply *
increases -----> + times ------> multiply
represent the numbers by variables such as x, y, z , w ....

then solve the equation by algebra.... PEMDAS in reverse :-) or by simultaneous equations in this assignment.

Try this on question #1

The sum of two numbers ...... x + y is = 103
x + y = 103
if you let x be the larger then
The larger no. is 1 more than 5 times the smaller
x = 5y + 1

you have 2 equations in 2 unknowns so solve as simultaneous equations (substitution is good here)
(5y + 1 ) + y = 103 hey you are almost there,,,,good luck !

Answer 2

1. x1 > x2
x1 + x2 = 103
x1 - 5 * x2 = 1
--> x1 = 5 * x2 + 1
--> 6 * x2 + 1 = 103
6 * x2 = 102
x2 = 17
x1 = 103 - 17 = 86


2. 2/3 * x - 1/2 * x = 3
1/6 * x = 3
x = 18


3. 5 * (x + 8) + 10 = 30 * x
5x + 40 + 10 = 30x
50 = 25x
x = 2


4. x * 6 - 5 = 31
6x = 36
x = 6


5. x + x/4 = 2x + 6 (is that what you mean?)
0 = 3/4x + 6
3/4x = -6
x = -8

Answer 3

1. well,we have two numbers x and z.
x+z=103 and x=5z+1
So, we have: 5z+1+z=103
6z+1=103
6z=103-1
6z=102
z=102/6
z=17

x=5 *17+1
x=85+1
x=86

2.We have the number x

1/2x=2/3x-3
3=2/3x+1/2x
3=4/6x+3/6x
3=7/6x
x=6/7*3
x=18/7

3. 5(x+8)=30x-10
5x+40=30x-10
5x-30x=-40-10
-25x=-50
x=-25/-40
x=2

4. 6x/5=31
6x=31*5
6x=155
x=155/6


5. x+x/4=2x+6
x+x/4-2x=6
-x+x/4=6
-4x/4+x/4=6
-3x/4=6
-3x=24
x=24/-3
x=-8

I wish I helped you!!!

Answer 4

1. suppose the numbers are a and b
a+b=103
b=5a+1
therefore a+(5a+1)=103
=a+5a+1= 6a+1=103
6a=103-1=102
a=102/6=17
b=5(17)+1=86

2.Suppose the number is a
1/2a=2/3a-3
3=(2/3-1/2)a
3=1/6a
a=3*6=18

3.Suppose the number is p
5(p+8)=30p-10
5p+40=30p-10
40+10=30p-5p
50=25p
p=50/25=2

4.Suppose the number is t
6t-5=31
6t=31+5=36
t=36/6=6

5. Suppose the integer is q
q+q/4=6+2q
q-2q+q/4=6
-3q/4=6
-3q=6*4=24
q=24/-3=-8

I hope this will do

Answer 5

1)

Here I go. x + 5x + 1 = 103
So 6x = 102
102 divided by 6 is 17 (one of the answers)
the other answer is the differece between 102 and 17 (86
To check; is 86 = (17x5)+1?
Yes

That was only the first question. I couldn't figure them all out.

4) 6x-5=31
Easy!
6x=36
x=6
The answer for question 4 is "6"

That's all I could do, sorry I'm no help.

Answer 6

1)
A+B=103
A=5B+1
5B+1=B=103
6B=102
B=17
A=103-17=86

2) (1/2)x=(2/3)x-3
(1/6)x=3
x=18

3) 5*(x+8)= 30X-10
25x=50
x=2

4) 6x-5=31
6x=36
x-6

5)x+(x/4)=6+2x
(3/4)x=-6
x=-8

hope this helps

Answer 7

1. Let the smaller no. be x . The larger no. = 5x+1

Sum of nos. = 103
5x+1+x=103
6x=102
x = 102/6
x = 17
Larger no. 86
and try the rest accordingly

Answer 8

a million. abs(x-three) = x-three for x >/= three abs(x-three) = three-x for x / = five/three abs(3x-five) = five-3x for x < five/three (x-three) ____ < / = 6 (3x-five) x-three