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4 years ago

How many 3-digit numbers can you write using only the digits 1 and 2?

1 answer:

defon4 years ago

4 0

For the first digit, you have two possible choices: 1 or 2. For *each* of those choices, you can choose 1 or 2 for the second digit in the number, and for each of *those*, you can choose 1 or 2 for the third digit of the number.

That’s 2 * 2 * 2 or 8 possible 3-digit numbers you can make with the digits 1 and 2.

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Solve.

abruzzese [7]

Answer:

$x=\frac{15}{4}=3\frac{3}{4}$

Equation:

$\frac{2}{3}x+\frac{5}{6} =\frac{10}{3}$

<h3>Step-by-step solution</h3>

Linear equations with one unknown

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1. Group all constants on the right side of the equation

$\frac{2}{3}\cdot x+\frac{5}{6}=\frac{10}{3}$

Subtract $5/6$ from both sides:

$\frac{2}{3}x+\frac{5}{6}-\frac{5}{6}=\frac{10}{3}-\frac{5}{6}$

Combine the fractions:

$\frac{2}{3}\cdot x+\frac{5-5}{6}=\frac{10}{3}-\frac{5}{6}$

Combine the numerators:

$\frac{2}{3}\cdot x+\frac{0}{6}=\frac{10}{3}-\frac{5}{6}$

Reduce the zero numerator:

$\frac{2}{3}\cdot x+0=\frac{10}{3}-\frac{5}{6}$

Simplify the arithmetic:

$\frac{2}{3}\cdot x=\frac{10}{3}-\frac{5}{6}$

Find the lowest common denominator:

$\frac{2}{3}\cdot x=\frac{10\cdot 2}{3\cdot 2}+\frac{-5}{6}$

Multiply the denominators:

$\frac{2}{3}\cdot x=\frac{10\cdot 2}{6}+\frac{-5}{6}$

Multiply the numerators:

$\frac{2}{3}\cdot x=\frac{20}{6}+\frac{-5}{6}$

Combine the fractions:

$\frac{2}{3}\cdot x=\frac{20-5}{6}$

Combine the numerators:

$\frac{2}{3}\cdot x=\frac{15}{6}$

Find the greatest common factor of the numerator and denominator:

$\frac{2}{3}\cdot x=\frac{5\cdot 3}{2\cdot 3}$

Factor out and cancel the greatest common factor:

$\frac{2}{3}\cdot x=\frac{5}{2}$

2. Isolate the x

$\frac{2}{3}\cdot x=\frac{5}{2}$

Multiply both sides by inverse fraction 3/2:

$\frac{2}{3}x\cdot \frac{3}{2}=\frac{5}{2}\cdot \frac{3}{2}$

Group like terms:

$\frac{2}{3}\cdot \frac{3}{2}x=\frac{5}{2}\cdot \frac{3}{2}$

Simplify the fraction:

$x=\frac{5}{2}\cdot \frac{3}{2}$

Multiply the fractions:

$x=\frac{5\cdot 3}{2\cdot 2}$

Simplify the arithmetic:

$x=\frac{15}{2\cdot 2}$

Simplify the arithmetic:

$x=\frac{15}{4}$

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Why learn this

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

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