there are a total of 120 counters in a box, there are only red counters and blue counters in the box. there are three times as many red as blue counters in the box. carl takes 1/3 of the red counters from the box. kerry takes 80% of the blue counters from the box. work out the ratio of the number of red counters to blue counters now in the box. give your ratio in its simplest form

Let blue counters = x

Red counters would be 3x ( three times as many)

first find the number of red and the number of blue counters:

3x + x = 120

4x = 120

x = 120/4

x = 30

There are 30 blue counters and 90 red counters.

Carl took 1/3 of the red, 90 / 3 = 30, so there were 60 red counters left

Kerry took 80% of the blue, 30 * 0.80 = 24, so there were 6 blue counters left

The ratio of red to blue would be 60: 6 which can be simplified to 10:1.

The ratio of the number of red counters to blue counters now in the box is 10:1.

What is a ratio?

A ratio is the simplest relation shown between two quantities, in the way x:y, read as "x is to y", and functions as x/y.

How to solve the question?

In the question, we are said that there are a total of 120 counters in a box, there are only red counters and blue counters in the box. there are three times as many red as blue counters in the box. Carl takes 1/3 of the red counters from the box. Kerry takes 80% of the blue counters from the box.

We are asked to work out the ratio of the number of red counters to blue counters now in the box.

We assume the initial number of blue counters in the box to be x.

Then, the initial number of red counters in the box = 3x {three times as many red as blue}.

Therefore, the initial ratio of red to blue = 3x:x = 3:1.

Now, Carl takes 1/3 of the red counters.

The number of red counters left = 3x - (1/3) of 3x = 3x - (1/3)*3x = 3x - x = 2x.

Also, Kerry takes 80% of the blue counters.

The number of blue counters left = x - 80% of x = x - 0.8x = 0.2x

Therefore, the final ratio of red to blue = 2x:0.2x = 10:1 (Simplest form).

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