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deff fn [24]
3 years ago
15

Sarah has a brother who is 5 years younger than herself and another brother who is 8 years younger than herself. She observes th

at the product of her brothers ages is equal to the age of her 40 year old father. How old is Sarah? How do we setup an equation for this using null factor law presumably.
Mathematics
1 answer:
ELEN [110]3 years ago
3 0

Answer:

Sarah is 13 years old

Step-by-step explanation:

Represent Sarah's age with S

Her first brother's age with F

Her second brother's age with B

So, we have:

From the first statement, we have:

S - F = 5 ---- (1)

From the second, we have:

S - B = 8 ---- (2)

The product of their ages is 40.

First, we make F the subject in (1) and B the subject in (2)

F = S - 5

B = S - 8

Their product is represented as follows:

F * B = 40

Substitute values for F and B

(S - 5) * (S - 8)=40

Open bracket

S^2 - 5S -8S + 40 = 40

S^2 - 13S + 40 = 40

Subtract 40 from both sides

S^2 - 13S = 0

Factorize:

S(S - 13) = 0

Split:

S = 0 or S - 13 = 0

But Sarah's age can't be 0 because she has two younger brothers.

So, we stick to

S - 13 = 0

Make S the subject

S = 13

<em>Hence, Sarah is 13 years old</em>

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andriy [413]
We are given that there are 11 animals with a total of 34 legs.

 Let G = number of Goats, and D = number of Ducks

 then G + D = 11; solving for G, we get G = 11 - D

 then, 4G + 2D = 34

 substituting the value for G, we get 4(11 - D) + 2D = 34

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3 years ago
The sum of two consecutive even numbers is 206. What is the value of the smallest number?
lesya692 [45]

Answer:

102

Step-by-step explanation:

Since we know that the numbers are two consecutive even numbers, we can write an equation like this where n represents the 2 numbers.

n + (n+2) = 206

Simplify the left side:

n + (n+2) = 206 -----> 2n+2 = 206

Subtract 2 from both sides:

2n = 206-2 -----> 2n = 204

Now divide 204 by 2:

n = 204/2 -----> n = 102

3 0
3 years ago
The sum of 139 and the product of a number raised to the third power and 17. In symbols, the phrase is written as.
qwelly [4]

Answer:

<u>y = 139 + x³ + 17 </u>

Step-by-step explanation:

The word "sum" means the amount resulting from addition in an equation. This means that we are adding all of these numbers together.

The word "product" means the amount resulting from multiplication in an equation, this means we need to find the product of a number multiplied by itself three times. Since we don't know what number it is, we can use the variable 'x'.

So, you would be adding 139, the product of x³, and 17, which would be written as y = 139 + x³ + 17.

7 0
2 years ago
Solve the following equation. 14 + (2x + 7) = 9x x=​
Dvinal [7]

Answer:

x=1

Step-by-step explanation:

14+2x+7=9x

2x-9x=7-14

-7x= -7

x= -7/-7

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2 years ago
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Zarrin [17]

Answer:

25

Step-by-step explanation:

5 cents = 0.05

1.25 / 0.05 = 25

let me know if i'm wrong

5 0
3 years ago
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