One fifth of a number plus three times the number is equal to twice the number plus 42 what is the number

The term "a number" is going to be our variable, and we will use x to express that unknown number. The term "of" can also mean multiply, so ...

One fifth of a number = 1/5x

Three times the number = 3x

Twice the number = 2x

Now we add the other components to complete the rest of the equation:

1/5x + 3x = 2x + 42

And then simplify the equation which comes down to:

x = 35

Let the number be n.

Then n/5 + 3n = 2n + 42

Mult. all terms by 5 to eliminate the fractional coefficient 1/5:

n + 5n = 210

Then 6n = 210, and n = 210/6 = 35

Check! Does (1/5) (35) + 3 (35) = 2 (35) + 42?

Does 7 + 105 = 70 + 42?

Does 112 = 112? YES

The number is 35.