Question

The sum of 3 1/4 and 2/3 of a number is the same as 1/4 of the number subtracted from 12 1/4 find the number

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Answer 1

3 1/4 + 2/3 * x = 12 1/4 - 1/4 * x

3 1/4 + 2/3 * x + 1/4 * x = 12 1/4

2/3 * x + 1/4 * x = 12 1/4 - 3 1/4

8/12 * x + 3/12 * x = 9

11/12 * x = 9

x = 9 * 12/11

x = 108/11

Answer 2

`9 (9)/(11)`

Explanation:

Let the unknown number be x.

Given equation:

`3 (1)/(4) + (2)/(3)x=12 (1)/(4)-(1)/(4)x`

`\textsf{Add\; $(1)/(4)x$ \;to\;both\;sides\;of\;the\;equation}:`

`\implies 3 (1)/(4) + (2)/(3)x+(1)/(4)x=12 (1)/(4)-(1)/(4)x+(1)/(4)x`

`\implies 3 (1)/(4) + (2)/(3)x+(1)/(4)x=12 (1)/(4)`

`\textsf{Subtract\; $3(1)/(4)$ \;from\;both\;sides\;of\;the\;equation}:`

`\implies 3 (1)/(4) + (2)/(3)x+(1)/(4)x-3 (1)/(4)=12 (1)/(4)-3 (1)/(4)`

`\implies (2)/(3)x+(1)/(4)x=12 (1)/(4)-3 (1)/(4)`

Subtract the mixed numbers:

`\implies (2)/(3)x+(1)/(4)x=9`

When adding fractions with different denominators, multiply the numerator and the denominator of each fraction by the same amount to make the denominators the same:

`\implies (4)/(4) \cdot (2)/(3)x+(3)/(3) \cdot (1)/(4)x=9`

`\implies (8)/(12)x+(3)/(12)x=9`

Add the fractions:

`\implies \left((8)/(12)+(3)/(12)\right)x=9`

`\implies (11)/(12)x=9`

Multiply both sides by 12:

`\implies 12 \cdot (11)/(12)x=12 \cdot 9`

`\implies 11x=108`

Divide both sides by 11:

`\implies (11x)/(11)=(108)/(11)`

`\implies x=(108)/(11)`

To convert the fraction into a mixed number, divide the numerator by the denominator:

`\implies 108 / 11 = 9\; \textsf{remainder}\;9`

The mixed number answer is the whole number and the remainder divided by the denominator:

`\implies x=9 (9)/(11)`