High School

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A bag contains only red, green and blue counters.

red counters : green counters : blue counters = 3 : 4 : 5

15 red counters and some blue counters are added to the bag. The ratio after this is shown below.

red counters : green counters : blue counters = 7 : 6 : 8

Work out the total number of counters in the bag after the red and blue counters were added.

A bag contains only red green and blue counters red counters green counters blue counters 3 4 5 15 red counters and some blue counters

Answer :

The total number of counters in the bag after the red and blue counters were added is 135.

Initially, the bag has 3x + 4x + 5x counters in total.

After adding 15 red counters, the number of red counters becomes 3x + 15, and the new ratio is 7:6:8. Setting up the equation:

(3x + 15) / (4x) = 7 / 6

Now, let's solve this equation:

6(3x + 15) = 4x * 7

18x + 90 = 28x

10x = 90

x = 9

Now that we know x, we can find the initial total number of counters:

3x + 4x + 5x = 12x = 12 * 9 = 108

So, initially, there are 108 counters in the bag.

After adding 15 red counters and some blue counters, the new total number of red counters is:

= 3x + 15 = 3 * 9 + 15

= 42.

The new total number of blue counters is the difference in the initial total and the number of red counters added:

108 - 15

= 93

Therefore, the total number of counters in the bag after the red and blue counters were added is

= 42 + 93

= 135.

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Rewritten by : Barada