Question

I thought of a number, I added 1 3 4 to it, then I multiplied the result by 2 2 11 and I got 8. What was my number?

Answer 1

Question:

I thought of a number, I added 1 3/4 to it, then I multiplied the result by 2 2/11 and I got 8. What was my number?

Answer:

The number is $1\frac{11}{12}$

Step-by-step explanation:

Let the number be x.

Analyzing the steps, 1 at a time

Add $1\frac{3}{4}$ to x

This implies:

$x + 1\frac{3}{4}$

Multiply by $2\frac{2}{11}$ to result in 8

This implies:

$(x + 1\frac{3}{4}) * 2\frac{2}{11} = 8$

Now, we solve for x

Convert mixed numbers to improper fractions

$(x + \frac{7}{4}) * \frac{24}{11} = 8$

$(\frac{4x + 7}{4}) * \frac{24}{11} = 8$

Multiply through by 11

$11 * (\frac{4x + 7}{4}) * \frac{24}{11} = 8 * 11$

$(\frac{4x + 7}{4}) * 24 = 88$

Divide through by 24

$(\frac{4x + 7}{4}) * 24/24 = 88/24$

$\frac{4x + 7}{4} = \frac{88}{24}$

Multiply through by 4

$4 * \frac{4x + 7}{4} = \frac{88}{24} * 4$

$4x + 7 = \frac{88 * 4}{24}$

$4x + 7 = \frac{88}{6}$

$4x + 7 = \frac{44}{3}$

Make 4x the subject

$4x = \frac{44}{3} -7$

$4x = \frac{44-21}{3}$

$4x = \frac{23}{3}$

Solve for x

$x = \frac{23}{3 * 4}$

$x = \frac{23}{12}$

$x = 1\frac{11}{12}$

Hence, the number is $1\frac{11}{12}$