Math questions, pleeeeeeeeeeeeeease answer...im going nuts with this..?

Question

a. If one half of a certain number be added to one third of the same number, the result is 35, what is the number?

b. Find 2 consecutive integers such that one - fourth the smaller is 3 more than one fifth the larger

c. the smaller of two numbers is 3/4 the larger. THe sum of the multiplicative inversed of the two numbers is 7/24. Find the two numbers.

please show the solution too..

thanks!!!

Answer 1

a.)
(1/2)x + (1/3)x = 35
Multiply everything by 6
3x + 2x = 210
5x = 210
x = 42

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b.)
(1/4)x = (1/5)(x + 1) + 3
Multiply everything by 20
5x = 4(x + 1) + 60
5x = 4x + 4 + 60
x = 64

ANS : 64 and 65

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c.)
x = (3/4)y
(1/x) + (1/y) = (7/24)

(1/((3/4)y))) + (1/y) = (7/24)
((1/1)/(3y/4)) + (1/y) = (7/24)
((1/1)*(4/(3y))) + (1/y) = (7/24)
(4/(3y)) + (1/y) = (7/24)

Multiply everything by 24y

32 + 24 = 7y
7y = 56
y = 8

x = (3/4)8
x = (24/4)
x = 6

ANS : 6 and 8

Answer 2

a.let the number be x
one half of it=1/2x
one third of the same number=1/3x
sum=35
the equation
1/2x+1/3x=35
LCD is 6,so multiplying by 6
(1/2)x*6+(1/3)x*6=35*6
3x+2x=210
5x=210
dividing by 5
5x/5=310/5
x=42

b.let the consecutive integers be x,x+1
1/4 th of the smaller=1/4x
1/5th of the larger=1/5(x+1)
1/4 th of the smaller is 3 more than 1/5th of the larger
the equation
1/4x=3+1/5(x+1)
multiplying throughout by 20,the LCD
(1/4)x*20=3(20)+(1/5)(x+1)20
5x=60+4x+4
adding -4x
5x-4x=64+4x-4x
x=64
the nos are 64,65
check
(1/4)*64=16
(1/5)*65=13
checks

c.let the smaller of the two numbers be x
let the larger be y
equation (1)
x=(3/4)y.....(1)
multiplicative inverses of thetwo numbers are 1/x and 1/y
sum of the multiplicative inverses is 7/24
the equation
1/x+1/y=7/24
multiplying by 24xy the LCD
24y+24x=(7/24)*24xy
24x+24y=7xy
substituting x=(3/4)y from (1)
24(3/4)y+24y=7(3/4)y*y
18y+24y=(21/4)y^2
42y=(21/4)y^2
dividing by y
42=(21/4)y
multiplying by 4/21
42(4/21)=(21/4)(4/21)y
8=y
substituting x=(3/4)*8
x=6
the nos are 6 and 8
check
6=(3/4)*8 checks
(1/6)+(1/8)=(4/24)+(3/24)=(7/24) checks

Answer 3

Answer 1:
Let the number be 'x'.
x/2 + x/3 = 35
3x/6 + 2x/6 = 35
5x/6 = 35
5x = 35*6
5x = 210
x = 210/5
x = 42
The number is 42

Answer 2:
Let the integers be 'x' and 'x+1'
x/4 = (x + 1)/5 + 3
x/4 = (x + 1)/5 + 15/5
x/4 = (x + 1 + 15)/5
5x/4 = x + 1 + 15
5x = 4x + 4 + 60
x = 64
x + 1 = 65
The integers are 64 and 65

Answer 4

a. let x be that number.
(1/2)x +(1/3)x = 35
(3/6)x + (2/6)x =35
(5/6)x = 35
5x=210
x=42

b.
let y and y+1 be those two numbers
1/4(y)= (1/5)(y+1) +3
y= (4/5) (y+1) +12
y= 4/5 y + 4/5 +12
1/5y = 64/5
y=64
y+1=65
so the two consecutive nubmers are 64 and 65

Answer 5

If you know algebra you should be able to solve this systematically. I'll solve the first part, then you should be able to do the rest:

a) let x = the number:
Here's the equation:
x/2 + x/3 = 35
5x/6= 35
multiply both sides by 6:
5x = (35*6 = 210)

Divide both sides by 5:

x=42

Answer 6

X= THE NUMBER

1/2x + 1/3x=35
MULTIPLY 6 TO BOTH SIDES OF THE EQUATION
3X + 2X = 210
SOLVE FOR X
X=42

problem solved!

for part b keep in mind the the term "is" means equal so you use that slight hint to set up your equation.

x= first integer
x + 1=second integer

see two consecutive int's
1/4x = 1/5(x+1) + 3
x= 64

Answer 7

Wouldn't do it even if I could. Do your own homework :)