Question

Three less than three times a number is 5/6. What is one more than twice the number

Answer 1

To solve the equation, first isolate the unknown number and then calculate 'one more than twice the number'. The process involves converting whole numbers to fractions, combining like terms, and simplifying. The final answer is one more than twice the number is 64/18.

Step-by-step explanation:

The question asks us to solve the equation 'three less than three times a number is 5/6' to find the number, and then to calculate 'one more than twice the number'. Let's denote the unknown number as n. The equation can be written as:

3n - 3 = 5/6

To solve for n, we would first add 3 to both sides:

3n = 5/6 + 3

Then, we convert 3 to a fraction with the same denominator:

3n = 5/6 + 18/6

Now we combine the fractions:

3n = 23/6

Next, divide both sides by 3 to isolate n:

n = 23/18

Now that we have the value of n, we can calculate 'one more than twice the number':

2n + 1 = 2(23/18) + 1

2n + 1 = 46/18 + 1

Convert 1 into a fraction with the same denominator:

2n + 1 = 46/18 + 18/18

Combine the fractions:

2n + 1 = 64/18

Thus, one more than twice the number is 64/18.

Answer 2

32/9

Step-by-step explanation:

Translating the word problem into a symbolic equation yields:

3n - 3 = 5/6

Solve this for the number (n):

Multiplying both sides of this equation by 6 clears out the fraction term:

18n - 18 = 5

Adding 18 to both sides isolates 18n: 18n = 23

Then the number is n = 23/18, and:

one more than twice this number n is 2(23/18) + 1, or:

46/18 + 18/18, or 64/18, or (reducing this result)

32/9