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 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
Let's solve this problem step by step.
Let's say the initial number of red pens is 3x and the initial number of blue pens is 4x, where x is a positive integer.
According to the given information, the ratio of the number of red pens to the number of blue pens is 3:4. So, we have the equation:
(3x)/(4x) = 3/4
Cross-multiplying:
3 * 4x = 3x * 4
12x = 12x
This equation is true, so any value of x would work. Since we need to find the final number of red and blue pens, we can choose any value for x.
Let's assume x = 1.
So, initially, there are:
Red pens = 3 * 1 = 3
Blue pens = 4 * 1 = 4
Now, Mr. Lim puts another 20 pens into the box, so the total number of pens becomes:
Total pens = 3 + 4 + 20 = 27
According to the newly formed ratio, the number of red pens to the number of blue pens is 2:1. So, we have the equation:
(number of red pens)/(number of blue pens) = 2/1
Let's assume the number of red pens is 2y and the number of blue pens is y (where y is a positive integer).
So, we have the equation:
(2y)/(y) = 2/1
Cross-multiplying:
2 * y = 1 * 2y
2y = 2y
This equation is true, so any value of y would work. Since we need to find the final number of red and blue pens, we can choose any value for y.
Let's assume y = 1.
So, in the end:
Number of red pens = 2 * y = 2 * 1 = 2
Number of blue pens = y = 1
Therefore, in the end:
(A) There are 2 red pens.
(B) There is 1 blue pen.
Let's solve this step-by-step:
Step 1: Set up the initial ratio equation.
The initial ratio of red pens to blue pens is 3:4.
This can be written as 3x:4x, where x is a common multiplier.
Step 2: Calculate the number of red and blue pens initially.
Let the initial number of red pens be 3x, and the initial number of blue pens be 4x.
Step 3: Add another 20 pens to the box.
Now, the total number of red pens becomes 3x + 20, and the total number of blue pens becomes 4x + 20.
Step 4: Set up the final ratio equation.
The new ratio of red pens to blue pens is 2:1.
This can be written as (3x + 20):(4x + 20).
Step 5: Solve the final ratio equation.
Since the final ratio is 2:1, we can set up the equation (3x + 20)/(4x + 20) = 2/1.
Step 6: Cross-multiply and solve for x.
(3x + 20) * 1 = (4x + 20) * 2.
3x + 20 = 8x + 40.
5x = 20.
x = 4.
Step 7: Calculate the number of red and blue pens in the end.
The number of red pens in the end is 3x + 20 = 3(4) + 20 = 12 + 20 = 32.
The number of blue pens in the end is 4x + 20 = 4(4) + 20 = 16 + 20 = 36.
Answer:
(A) There are 32 red pens in the end.
(B) There are 36 blue pens in the end.
To solve this question, we can use algebraic equations and ratios.
Let's start by representing the number of red pens and blue pens initially as 3x and 4x respectively. The ratio of red pens to blue pens is 3:4, so the total number of pens in the box initially is 3x + 4x = 7x.
Mr. Lim then adds 20 more pens to the box. The ratio of red pens to blue pens becomes 2:1, which means the total number of pens in the box after adding the 20 pens is 2y + y = 3y, where y is the number of blue pens in the end.
Now we have two equations:
Equation 1: (number of red pens) + (number of blue pens) = (total number of pens)
Equation 2: 3x + 4x + 20 = 3y
Simplifying equation 2, we get:
7x + 20 = 3y
Since we're interested in finding the number of red and blue pens, we need to solve for both x and y.
(A) To find the number of red pens in the end, we need to solve for x. From equation 1, we know that the number of red pens is 3x. We can use equation 2 to find the value of x.
7x + 20 = 3y
Now, we need to look for values of x that satisfy this equation. Let's assume that x = 1, then we get:
7(1) + 20 = 3y
7 + 20 = 3y
27 = 3y
y = 27/3
y = 9
So, if x = 1, then y = 9. This means that there are 9 blue pens in the end.
Now, to find the number of red pens (3x):
3(1) = 3
Therefore, there were 3 red pens in the end.
(B) To find the number of blue pens in the end, we have already determined that there are 9 blue pens.