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 [tex]1\frac{11}{12}[/tex]
Step-by-step explanation:
Let the number be x.
Analyzing the steps, 1 at a time
Add [tex]1\frac{3}{4}[/tex] to x
This implies:
[tex]x + 1\frac{3}{4}[/tex]
Multiply by [tex]2\frac{2}{11}[/tex] to result in 8
This implies:
[tex](x + 1\frac{3}{4}) * 2\frac{2}{11} = 8[/tex]
Now, we solve for x
Convert mixed numbers to improper fractions
[tex](x + \frac{7}{4}) * \frac{24}{11} = 8[/tex]
[tex](\frac{4x + 7}{4}) * \frac{24}{11} = 8[/tex]
Multiply through by 11
[tex]11 * (\frac{4x + 7}{4}) * \frac{24}{11} = 8 * 11[/tex]
[tex](\frac{4x + 7}{4}) * 24 = 88[/tex]
Divide through by 24
[tex](\frac{4x + 7}{4}) * 24/24 = 88/24[/tex]
[tex]\frac{4x + 7}{4} = \frac{88}{24}[/tex]
Multiply through by 4
[tex]4 * \frac{4x + 7}{4} = \frac{88}{24} * 4[/tex]
[tex]4x + 7 = \frac{88 * 4}{24}[/tex]
[tex]4x + 7 = \frac{88}{6}[/tex]
[tex]4x + 7 = \frac{44}{3}[/tex]
Make 4x the subject
[tex]4x = \frac{44}{3} -7[/tex]
[tex]4x = \frac{44-21}{3}[/tex]
[tex]4x = \frac{23}{3}[/tex]
Solve for x
[tex]x = \frac{23}{3 * 4}[/tex]
[tex]x = \frac{23}{12}[/tex]
[tex]x = 1\frac{11}{12}[/tex]
Hence, the number is [tex]1\frac{11}{12}[/tex]
