Arjun spent Rs.12 to purchase some pens and pencils.The cost of a pen and pencil are in the ratio 3:2.
the total cost of a pen and a pencil is Rs. 3.
if the total number of pens and pencils he purchased is7,
find the number of pens he purchased.
let the cost of a pen be 3x
let the cost of a pencil be 2x , ( notice 3x : 2x = 3:2 )
number of pens --- a
number of pencils --- 7-a , because their sum is 7
3x + 2x = 3
5x = 3
x = Rs 3/5 = Rs 0.6
so a pen costs Rs 1.8
and a penci costs Rs 1.2
1.8a + 1.2(7-a) = 12
1.8a + 8.4 - 1.2a = 12
.6a = 3.6
a = 6
so there were 6 pens purchased and 1 pencil
check:
1+6 = 7 , number of pens and pencils checks!
cost of pen = 1.8
cost of pencil = 1.2
ratio is 1.8 : 1.2 = 3 : 2 , ratio costs checks!
6pens + 1 pencil = 6(1.8) + 1.2 = 12
All looks good!
Let's assume the number of pens Arjun purchased is 'x'.
According to the given information, the cost ratio of a pen to a pencil is 3:2.
So, the cost of a pen is 3/5 of Rs. 3.
Therefore, the cost of a pen is (3/5) * 3 = Rs. 9/5.
Let's use the given information to form an equation:
The total cost of a pen and a pencil is Rs. 3.
So, (9/5)x + (2/5)(7 - x) = 3.
Multiplying both sides of the equation by 5 to get rid of the denominators, we have:
9x + 2(7 - x) = 15.
Expanding the equation, we get:
9x + 14 - 2x = 15.
Combining like terms, we have:
7x + 14 = 15.
Subtracting 14 from both sides of the equation, we get:
7x = 1.
Dividing both sides of the equation by 7, we get:
x = 1/7.
So, the number of pens Arjun purchased is 1/7.
Please note that there seems to be an inconsistency in the given information, as it states that the total cost of a pen and a pencil is Rs. 3, but based on the cost ratio, the total cost should be Rs. 3.80, not Rs. 3.
To find the number of pens Arjun purchased, we can first set up a system of equations based on the given information.
Let's say the number of pens Arjun purchased is "x".
Since the cost ratio of pens to pencils is 3:2, we can set up the equation:
Cost of pens = 3 * x
Similarly, if the cost of a pencil is represented by "y", we can write:
Cost of pencils = 2 * y
The total cost of a pen and a pencil is Rs. 3, so we have:
3 * x + 2 * y = 3
We are also told that the total number of pens and pencils purchased is 7. Therefore, we can write another equation:
x + y = 7
Now we have a system of two equations with two variables:
3 * x + 2 * y = 3
x + y = 7
We can solve this system of equations to find the value of "x", which represents the number of pens Arjun purchased.