A bag contains only red and blue marbles. There are a total of 36 marbles in the bag. There are 5 red marbles for every 4 blue marbles in the bag. Carl removes 1 blue marble from the bag. Carl says, “There are now 5 red marbles for every 3 blue marbles in the bag because 4 – 1 = 3.”
Explain the error in Carl’s reasoning. Calculate the correct ratio of red to blue marbles after Carl removes 1 blue marble, and be sure to include this in your explanation.

let total no. of red marbles be x and blue marbles be y.

then according to first case

x + y =36

or,x=36 -y(i)

in case second

x/5 =y/4

or,x=5y/4(ii)

then from equation i and ii, we get

36-y = 5y/4

or, (36-y)4 = 5y

or, 144 -4y =5y

or, 144 = 5y + 4y

or, 144 = 9y

or, 144/9 =y

or, y = 16

again x = 36 -y

here , y =16

so,

x= 36 -16

x= 20.

hence total no. of red marbles is 20 and blue marbles is 16 .

If Carls removes 1 blue marble from bag, there will be 15 marbles in the bag,

20÷5 is not equal to 15 ÷3 .

correct ratio of red and blue marbles is 20÷15=

4/3.

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

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