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3 years ago

How can you use proportional reasoning to solve problems involving percent

1 answer:

3 0

Example A, Step 1: Write a comparing the percent to the ratio of part to whole. ex- ?/25 = 28/100 *Notice that 25 is a factor of 100* Step 2: Find the multiplication factor. ex- ?*4 = 28 and 25*4 = 100 *Since 25*4 = 100, find what number times 4 equals 28* Step 3: Find the numerator. ex- 7/25 = 28/100 *Since 4*7 = 28, 28% of 25 = 7 Example B, Step 1: Write the percent as a fraction. ex-35% of 60 = 35/100 of 60 Step 2: Multiply. ex- 35/100 of 60 = 35/100x60=2100/100=21 *Simplify* Example C, Step 1: Write the percent as a decimal. ex- 5% = 5/100 = 0.05 Step 2: Multiply. ex- 180 * 0.05 = 9, 5% of 180 is 9.

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Simplify 1)5x+3=x+13 2)5/2x-1/X =1/6

Artyom0805 [142]

Step-by-step explanation (Question 1):

Step 1: (Question 1): Subtract x from both sides.

5x+3=x+13

5x+3−x=x+13−x

4x+3=13

Step 2: (Question 1): Subtract 3 from both sides.

4x+3−3=13−3

4x=10

Step 3: (Question 1): Divide both sides by 4.

4x/4 = 10/4

FIRST ANSWER: x = 5/2

Step-by-step explanation (Question 2):

Step 1: (Question 2): Multiply by LCM

15x^2 - 6 = x

Step 2: (Question 2): Solve 15x^2

15x^2 - 6 = x:

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Step 3: (Question 2): Solve

ANSWER: x=0.666667 or x=−0.6

See Attachment 1 for question 1 steps (FULL)

See Attachment 2 for question 2 steps (FULL)

Answer:

1) x = 5/2

2) x=0.666667 or x=−0.6

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2 years ago

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(4x + 4)(ax – 1) – x2 +4

Oksana_A [137]

Answer:

b=-3

Step-by-step explanation:

If the expression simplifies to bx that means the $x^{2}$ terms and the constant terms must be cancel out.

Simplify it first.

$(4x+4)(ax-1)-x^{2} +4\\=(4ax^{2} -4x+4ax-4)-x^{2} +4\\=4ax^{2} -x^{2} -4x+4ax-4+4\\=4ax^{2} -x^{2} -4x+4ax$

We know –4 + 4 will cancel out. If we simplify this expression to only an x term, then the $x^{2}$ terms should be cancelled. Therefore, we say that 4ax^2 – x^2 = 0.

$4ax^{2} -x^{2} =0\\x^{2} (4a-1)=0\\4a-1=0\\4a=1\\a=\frac{1}{4}$

If we put a = ¼, then we can find the value of b:

$=4(\frac{1}{4} )x^{2} -x^{2} -4x+4(\frac{1}{4} )x\\=x^{2} -x^{2} -4x+x\\ (cancel out x^{2} terms)\\$

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$bx=-3x\\$ if the expression is equivalent to bx

Therefore, b = –3.

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2 years ago