Question

There are some red counters and some yellow counters in a bag in the ratio 1 : 5

There are 20 yellow counters in the bag.

Janet puts some more red counters into the bag.

The ratio of the number of red counters to the number of yellow counters is now 1 : 2
How many red counters does Janet put into the bag​

Answer 1

Answer:

my ratio is 20 : 50

Step-by-step explanation:

Answer 2

Given:

Ratio of red counters to yellow counters in the bag = 1:5

No. of yellow counters = 20

Ratio of red counters to yellow counters after Janet puts some more red counters = 1:2

To find:

The no. of red counters Janet puts into the bag.

Solution:

Let the no. of red counters be $R$ and the no. of yellow counters be $Y$ in the bag.

The ratio of red counters to yellow counters in the bag is given as $1:5$.

$\frac{R}{Y}=\frac{1}{5}$

The no. of yellow counters is given as $20$. Substitute this value in the ratio above:

$\frac{R}{20}=\frac{1}{5}$

$R=\frac{20}{5}=4$

∴ There are 4 red counters initially.

Let $x$ be the no. of red counters put in by Janet into the bag. Now, the no. of red counters in the bag is $R+x$. The ratio of red counters to yellow counters in the bag after $x$ no. of red counters are put in the bag is given as $1:2$. There is no change in the no. of yellow counters, hence it remains as $Y$ itself.

$\frac{R+x}{Y}= \frac{1}{2}$

Now, $R$ is calculated as $4$ in number and $Y$ is given as $20$. Substituting in the above ratio:

$\frac{4+x}{20}=\frac{1}{2}$

On cross-multiplying,

$20=8+2x$

$20-8=2x$

$12=2x$

$x=\frac{12}{2}=6$

∴ Janet put 6 more red counters into the bag in addition to the 4 red counters that were initially in the bag.

Janet put 6 more red counters into the bag in addition to the 4 red counters that were initially in the bag.