Question

The ratio of the number of marbles in the red bag to the number in the blue bag is 3 : 5

Two marbles are moved from the blue bag to the red bag, making the ratio 7 : 9.

How many marbles are there in total?

Answer 1

answer: 16

step by step explanation:

Answer 2

The total number of marbles = 32 marbles.

We have ratio of the number of marbles in the red bag to the number in the blue bag is 3 : 5. After that, two marbles are moved from the blue bag to the red bag, making the ratio 7 : 9.

We have to find out how many marbles are there in total.

Is the ratio a:b equal to $\frac{a}{b}$.

Yes, a:b equals to $\frac{a}{b}$ - where ' a ' is called Antecedent and ' b ' is called Consequent.

Let the total number of marbles be x.

Let the number of marbles in the red bag be ' x ' and in blue bag ' y '.

According to question -

$\frac{x}{y} =\frac{3}{5}$

5x = 3y

x = $\frac{3y}{5}$

After the two marbles are moved from blue bag are moved into the red bag, then -

$\frac{x+2}{y-2} =\frac{7}{9}$

9(x + 2) = 7(y - 2)

9x + 18 = 7y - 14

9x - 7y = -32

9 ($\frac{3y}{5}$) - 7y = -32

$\frac{27y}{5} - 7y =-32$

$\frac{-8y}{5}=-32$

-8y = -32 x 5

y = 4 x 5

y = 20

Therefore -

x = $\frac{3\times20}{5}$ = 12

Hence, the total number of marbles = x + y = 20 + 12 = 32 marbles.

To solve more question on ratio, visit the link below -

https://brainly.com/question/28026128

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