Question

17

Jamal has some counters in a bag.

36% of the counters are red the rest of the counters are yellow

Jamal puts 50 blue counters into the bag. Now 25% of the counters in the bag are blue.

Work out the number of yellow counters in the bag.

Answer 1

Let's denote the total number of counters in the bag before adding the blue counters as T.

Initially, 36% of T counters are red, and the rest, which is 100, are yellow.

So, initially, the number of yellow counters is 0.64×T.

When Jamal adds 50 blue counters, the total number of counters becomes T+50.

Now, 25% of the counters in the bag are blue, so the number of blue counters is 0.25×(T+50).

Since the total number of counters is the sum of red, yellow, and blue counters, we can write the equation:

0.36×T+0.64×T+0.25×(T+50)=T+50

Now, let's solve for T to find the initial total number of counters:

0.36T+0.64T+0.25T+12.5=T+50

Combine like terms:

1.25T+12.5=T+50

Subtract T from both sides:

0.25T+12.5=50

Subtract 12.5 from both sides:

0.25T=37.5

Divide by 0.25:

T=150

So, initially, there were 150 counters in the bag. Now we can find the number of yellow counters:

0.64×150=96

Therefore, there were initially 96 yellow counters in the bag.