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

Answer:

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

Answer:

$9 \dfrac{9}{11}$

Step-by-step explanation:

Let the unknown number be x.

Given equation:

$3 \dfrac{1}{4} + \dfrac{2}{3}x=12 \dfrac{1}{4}-\dfrac{1}{4}x$

$\textsf{Add\; \dfrac{1}{4}x \;to\;both\;sides\;of\;the\;equation}:$

$\implies 3 \dfrac{1}{4} + \dfrac{2}{3}x+\dfrac{1}{4}x=12 \dfrac{1}{4}-\dfrac{1}{4}x+\dfrac{1}{4}x$

$\implies 3 \dfrac{1}{4} + \dfrac{2}{3}x+\dfrac{1}{4}x=12 \dfrac{1}{4}$

$\textsf{Subtract\; 3\dfrac{1}{4} \;from\;both\;sides\;of\;the\;equation}:$

$\implies 3 \dfrac{1}{4} + \dfrac{2}{3}x+\dfrac{1}{4}x-3 \dfrac{1}{4}=12 \dfrac{1}{4}-3 \dfrac{1}{4}$

$\implies \dfrac{2}{3}x+\dfrac{1}{4}x=12 \dfrac{1}{4}-3 \dfrac{1}{4}$

Subtract the mixed numbers:

$\implies \dfrac{2}{3}x+\dfrac{1}{4}x=9$

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:

$\implies \dfrac{4}{4} \cdot \dfrac{2}{3}x+\dfrac{3}{3} \cdot \dfrac{1}{4}x=9$

$\implies \dfrac{8}{12}x+\dfrac{3}{12}x=9$

Add the fractions:

$\implies \left(\dfrac{8}{12}+\dfrac{3}{12}\right)x=9$

$\implies \dfrac{11}{12}x=9$

Multiply both sides by 12:

$\implies 12 \cdot \dfrac{11}{12}x=12 \cdot 9$

$\implies 11x=108$

Divide both sides by 11:

$\implies \dfrac{11x}{11}=\dfrac{108}{11}$

$\implies x=\dfrac{108}{11}$

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

$\implies 108 \div 11 = 9\; \textsf{remainder}\;9$

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

$\implies x=9 \dfrac{9}{11}$