Mr Lim put some red pen and blue pen into a box the ratio of number of red pen to the number of blue pen was 3:4 he put another 20 red pens into the box and the ratio became 2:1

Question

Mr Lim put some red pen and blue pen into a box the ratio of number of red pen to the number of blue pen was 3:4 he put another 20 red pens into the box and the ratio became 2:1

(A) how many red pens were there in the end
(B) how many blue pens were there

Answer 1

Let's assume that the number of red pens in the beginning was 3x, and the number of blue pens was 4x.

After Mr. Lim put 20 red pens into the box, the number of red pens became 3x + 20. The number of blue pens remained the same, 4x.

According to the problem, the ratio after adding the red pens became 2:1. This means that (3x + 20)/(4x) = 2/1.

To solve for x, we can cross multiply: 2(4x) = (3x + 20)(1)

8x = 3x + 20

Subtract 3x from both sides: 5x = 20

Divide by 5: x = 4

So, the initial number of red pens was 3x = 3(4) = 12.

(A) The number of red pens in the end was 3x + 20 = 3(4) + 20 = 12 + 20 = 32.

(B) The number of blue pens remained the same, 4x = 4(4) = 16.

Answer 2

Let's solve this step by step:

Step 1: Set up equations for the given information.

Let R be the number of red pens and B be the number of blue pens in the box.

From the first statement, we know that the ratio of red pens to blue pens is 3:4, which can be expressed as:
R/B = 3/4

From the second statement, we know that after adding 20 red pens, the new ratio of red pens to blue pens is 2:1, which can be expressed as:
(R + 20) / B = 2/1

Step 2: Solve the equations simultaneously.

We can rearrange both equations to isolate R. First, let's rearrange the first equation:
R = (3/4)B

Now, let's rearrange the second equation:
(R + 20) = (2/1)B

Step 3: Substitute the first equation into the second equation.

Substitute (3/4)B for R in the second equation:
(3/4)B + 20 = (2/1)B

Step 4: Solve for B.

Multiply both sides by 4 to get rid of the fraction:
3B + 80 = 8B

Subtract 3B from both sides:
80 = 5B

Divide both sides by 5:
B = 16

Step 5: Substitute the value of B into the first equation to find R.

R = (3/4) * 16
R = 12

Therefore, in the end, there are 12 red pens and 16 blue pens in the box.

Answer:
(A) There are 12 red pens in the end.
(B) There are 16 blue pens in the end.

Answer 3

To solve this problem, we can set up algebraic equations based on the given information and use those equations to find the number of red and blue pens in the end.

Let's start by assigning variables to the unknown quantities. Let R be the number of red pens and B be the number of blue pens.

From the given information, we know that initially the ratio of red pens to blue pens was 3:4. So we can write the equation:

R/B = 3/4

We are also told that Mr Lim added 20 red pens to the box. After adding the red pens, the new ratio became 2:1. So we can set up another equation:

(R + 20) / B = 2/1

Now we have a system of two equations. We can solve it using algebraic methods:

First, let's rearrange the first equation to solve for R:
R = (3/4)B

Substitute this value of R into the second equation:
((3/4)B + 20) / B = 2/1

Now, cross-multiply:
2((3/4)B + 20) = B

Expand and simplify the equation:
(3/2)B + 40 = B

Now, bring the terms with B to one side:
(3/2)B - B = -40

Simplify:
(-1/2)B = -40

Multiply by -2 to isolate B:
B = (-40) * (-2) = 80

Now, substitute the value of B back into the first equation to find R:
R = (3/4) * 80 = 60

So, in the end:
(A) There were 60 red pens.
(B) There were 80 blue pens.