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lana66690 [7]
3 years ago
7

6/a - 4/b = 1 and 9/a - 8/b = 1​

Mathematics
1 answer:
Alja [10]3 years ago
5 0

Answer:

a = 3 ; b = 4

Step-by-step explanation:

Eqn.1 = \frac{6}{a}  -  \frac{4}{b}  = 1

Eqn.2 = \frac{9}{a}  -  \frac{8}{b}  = 1

Both the eqns have RHS (Right Hand Side) equal. So,

\frac{6}{a}  -  \frac{4}{b}  =  \frac{9}{a}  -  \frac{8}{b}

=  >  \frac{6b - 4a}{ab}  =  \frac{9b - 8a}{ab}

Cancelling ab from both the denominators of both the sides,

=  > 6b - 4a = 9b - 8a

=  > 8a - 4a = 9b - 6b

=  > 4a = 3b

=  > a =  \frac{3b}{4}

Putting the value of a in Eqn.1,

\frac{6}{ \frac{3b}{4} }  -  \frac{4}{b}  = 1

=  >  \frac{24}{3b}  -  \frac{4}{b}  = 1

=  >  \frac{8}{b} -  \frac{4}{b}   = 1

=  >  \frac{8 - 4}{b}  = 1

=  > b = 4

Putting the value of b in the value of a

a =  \frac{3 \times 4}{4}  = 3

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3 years ago
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Mice21 [21]

Answer:

There are 13 families had a parakeet only

Step-by-step explanation:

* Lets explain the problem

- There are 180 families

- 67 families had a dog

- 52 families had a cat

- 22 families had a dog and a cat

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- 4 had a​ cat, a​ dog, and a parakeet (4 is a part of 22 and 22 is a part

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* We will explain the Venn-diagram

- A rectangle represent the total of the families

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- The common part of the three circle had 4 families

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- The common part between the circle of the dog and the circle of the

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- The common part between the circle of the cat and the circle of the

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- The non-intersected part of the circle of the dog had 67 - 22 - a =

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  had dogs only

- The non-intersected part of the circle of the cat had 52 - 22 - b =  

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  had cats only

- The non-intersected part of the circle of the parakeet had c families

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- The part out side the circles and inside the triangle has 70 families

- Look to the attached graph for more under stand

∵ The total of the families is 180

∴ The sum of all steps above is 180

∴ 45 - a + 18 + 4 + 30 - b + b + c + a + 70 = 180 ⇒ simplify

- (-a) will cancel (a) and (-b) will cancel (b)

∴ (45 + 18 + 4 + 30 + 70) + (-a + a) + (-b + b) + c = 180

∴ 167 + c = 180 ⇒ subtract 167 from both sides

∴ c = 180 - 167 = 13 families

* There are 13 families had a parakeet only

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PLEASE HELP ME!!Write the quotient as a mixed number.<br> 46 divided by 9 = 5 R1
Zigmanuir [339]

Answer:

5\frac{1}{9}

Step-by-step explanation:

When dividing 46 by 9 quotient is 5 and remainder is 46 - 45 = 1

5\frac{1}{9}

5 0
3 years ago
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