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Misha Larkins [42]
3 years ago
7

The sum of the ages of Berma, her mother Rinna and her father Erwin is 80. Two years from now, Rinna’s age will be 13 less than

the sum of Erwin’s age and twice Berma’s age. Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. How old are they now?
Mathematics
1 answer:
jekas [21]3 years ago
6 0

Answer: Berma is 5 years old

Rinna is 38 years old

Erwin is 37 years old

Step-by-step explanation:

Let x represent Berma's age

Let y represent Rinna's age

Let z represent Erwin's age

Since the sum of their ages is 80,

x + y + z = 80 - - - - - - -1

Two years from now, Rinna’s age will be 13 less than the sum of Erwin’s age and twice Berma’s age. This means that

y +2 = [ (z+2) + 2(x+2) ] - 13

y +2 = z + 2 + 2x + 4 - 13

2x - y + z = 13 + 2 - 4 -2

2x - y + z = 9 - - - - - - -2

Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. It means that

15(x - 3) = (y - 3) - 5

15x - 45 = y - 3 - 5

15x - y = - 8 + 45

15x - y = 37 - - - - - - - -3

From equation 3, y = 15x - 37

Substituting y = 15x - 37 into equation 1 and equation 2, it becomes

x + 15x - 37 + z = 80

16x + z = 80 + 37 = 117 - - - - - - 4

2x - 15x + 37 + z = 9

-13x + 2 = -28 - - - - - - - - -5

subtracting equation 5 from equation 4,

29x = 145

x = 145/29 = 5

y = 15x - 37

y = 15×5 -37

y = 38

Substituting x= 5 and y = 38 into equation 1, it becomes

5 + 38 + z = 80

z = 80 - 43

z = 37

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Answer:

(a) Rule: Multiply the input (x) by 2 and add 5 to the result of the product

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Step-by-step explanation:

Given

The attached table

Solving (a): The rule of the table in words

First, we calculate the slope (m)

m = \frac{y_2 - y_1}{x_2 - x_1}

Using:

(x_1,y_1) =  (2,9)

(x_1,y_1) =  (10,25)

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The equation is calculated using:

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Using:

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Multiply the input (x) by 2 and add 5 to the result of the product

(b): The rule, in algebra

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Roberto rowed 20 miles downstream in 2.5 hours. The trip back, however, took him 5 hours. Find the rate that Roberto rows in sti
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Answer:

<em>Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour</em>

Step-by-step explanation:

<u>Relative Speed</u>

When a body is moving at a constant speed v, the distance traveled in a time t is:

d=v.t

When Roberto rows downstream, his speed in still water is added to the speed of the water, making it easier to travel the required distance.

When Roberto rows upstream, his speed in still water is affected by the speed of the water, both are subtracted and the required distance is covered in more time.

Let's call

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Rearranging, we find the downstream equation:

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Where t2=5 hours. Substituting values:

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Rearranging, we find the upstream equation:

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Solving for y

y=x-4=6-4=2

Thus, Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour

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