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Simora [160]
4 years ago
13

Any smart people out there, i really suck at these problems... Five times Lauren's age, decreased by 2 is equal to two times Lau

ren's age, increased by 11. How old is Lauren?
Mathematics
2 answers:
Fittoniya [83]4 years ago
5 0
Set Lauren's age equal to L.


Using what the problem gave us, we can quickly set up an equation: 

5L - 2 = 2L

Solving this equation, we get 3L = 2. L = 2/3 Lauren is 2/3 of a year old.
GrogVix [38]4 years ago
4 0

Take it slowly, one step at a time.

First, you need to pick something to call "Lauren's age",
because you don't know what number it is.  I have a bright idea ! 
Let's call Lauren's age ' L ' !  OK ?

Use ' L ' to build the quantities discussed in the question:

Five times Lauren's age . . . . . . . . . . . . . . . . . 5 L
Five times Lauren's age, decreased by 2 . . . 5L - 2

Two times Lauren's age . . . . . . . . . . . . . . . . .  2 L
Two times Lauren's age, increased by 11 . . . 2L + 11

The question says that these 2 quantities are equal,
so write that down:
                                                      5L - 2  =  2L + 11

Add  2  to each side:                  5L        =  2L + 13

Subtract  2L  from each side:    3L        =           13

Divide each side by  3 :                L        =           13/3  or  4 and 1/3 .

That's certainly a weird number, but you can
check it out, and you'll find that it's true:

Lauren's age . . . . . 13/3

Five times Lauren's age . . . . . . . . . . . . . . . . . 65/3
Five times Lauren's age, decreased by 2 . . . 59/3    <===

Two times Lauren's age . . . . . . . . . . . . . . . . .  26/3
Two times Lauren's age, increased by 11 . . . 59/3    <===

Those 2 quantities are equal.  So Lauren is 4-1/3 years old, by golly !

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3 years ago
Find the central angle of a sector of a circle of the area of the sector and the area of the circle are in the proportion of 3:5
abruzzese [7]

Answer:

\theta = 216

Step-by-step explanation:

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Area of Sector : Area of Circle = 3 : 5

Required

Determine the central angle

The question implies that

\frac{Area_{sector}}{Area_{circle}} = \frac{3}{5}

Multiply both sides by 5

5 * \frac{Area_{sector}}{Area_{circle}} = \frac{3}{5} * 5

5 * \frac{Area_{sector}}{Area_{circle}} = 3

Multiply both sides by Area{circle}

5 * \frac{Area_{sector}}{Area_{circle}} * Area_{circle} = 3 * Area_{circle}

5 * {Area_{sector} = 3 * Area_{circle}

Substitute the areas of sector and circle with their respective formulas;

Area_{sector} =\frac{\theta}{360} * \pi r^2

Area_{circle} = \pi r^2

So, we have

5 * \frac{\theta}{360} * \pi r^2 = 3 * \pi r^2

Divide both sides by \pi r^2

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5 * \frac{\theta}{360} = 3

Multiply both sides by 360

360 * 5 * \frac{\theta}{360} = 3 * 360

5 * \theta = 3 * 360

Divide both sides by 5

\frac{5 * \theta}{5} = \frac{3 * 360}{5}

\theta = \frac{3 * 360}{5}

\theta = \frac{1080}{5}

\theta = 216

Hence, the central angle is 216 degrees

3 0
3 years ago
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