Question

twice a number is as much greater than 30 as the three times of the number less than 60.find the number.

Answer 1

Let the number be x. "Three times a number increased by 10" is mathematically translated as 

3x + 10 

"is equal" is mathematically translated as 

= 

"Twenty less than six times the number" is mathematically translated as 

6x - 20 

The whole sentence "Three times a number increased by ten is equal to twenty less than six times the number" is translated as 

3x + 10 = 6x - 20 

We now solve the above linear equation to find the number x 

3x - 6x = - 20 - 10 

- 3x = - 30 

x = 10 

Check answer 

Three times a number increased by ten : 3 × 10 + 10 = 40 

Twenty less than six times the number : 6 × 10 - 20 = 40
If twice the difference of a number and 3 is added to 4, the result is 22 more than four times the number. Find the number. 

Solution 

Let the number be x. "twice the difference of a number and 3 is added to 4" is mathematically translated as 

2(x - 3) + 4 

"the result is" is mathematically translated as 

= 

"22 more than four times the number" is mathematically translated as 

4x + 22 

"twice the difference of a number and 3 is added to 4, the result is 22 more than four times the number" is mathematically translated as 

2(x - 3) + 4 = 4x + 22 

Solve the equation 

2x - 6 + 4 = 4x + 22 

2x - 4x = 22 - 4 + 6 

-2x = 24 

x = -12