find a number such that 10 less than two-thirds the number is one-forth the number

Question

I need to know how to solve it and the answer. this includes the equation(s) with the variable

 

Answer 1

(2x/3) - 10 = (x/4)

 

Multiply by 3:

 

2x - 30 = (3x/4)

 

Multiply by 4:

 

8x - 120 = 3x

 

x(8-3) = 120

 

5x = 120

 

x = 24

Answer 2

I could be wrong, but if the number is x, then my best guesstimate would be...

 

x(2/3)-10=x(1/4)

 

Solve for x either as a fraction or a decimal.

 

Divide by x on both sides...

 

(2/3)-(10/x)=(1/4)

 

(-10/x)=(1/4)-(2/3)

 

(-10/x)=-0.4167

 

Divide both sides by -10...

 

(1/x)=0.04167

 

Take the inverse of both sides...

 

x=(1/0.04167)

 

x=24

 

Check your answer by substituting 24 for x in the original equation...

 

24(2/3)-10=24(1/4)

 

(8)(2)-10=(6)(1)

 

16-10=6, or...

6=6, TRUE

 

Therefore, x=24.

 

Make sense?

 

 

Answer 3

let x= the number

(2/3)x-10=(1/4)x

(2/3)x-(1/4)x=10

(8/12)x-(3/12)x=10

(5/12)x=10

(12/5)(5/12)x=(12/5)(10)

x=120/5

x=24

check: (2/3)(24)-10=(1/4)(24)

                     16-10=6

                            6=6

 

Answer 4

Hi Izzy;

[(2/3)x]-10=(1/4)(x)

Let's eliminate the fractions.

The denominators are 3 and 4.

(3)(4)=12

Let's multiply both sides by 12...

12{[(2/3)x]-10}=(1/4)(x)(12)

8x-120=3x

Let's subtract 8x from both sides...

-8x+8x-120=3x-8x

-120=-5x

Let's divide both sides by -5...

-120/-5=(-5x)/-5

24=x

 

Let's check our results...

 

[(2/3)x]-10=(1/4)(x)

[(2/3)(24)]-10=(1/4)(24)

16-10=6

6=6