Divya has pens and pencils which are 60 in number. If she has 25 more pens and 5 less pencils, then the number of pens become three times the number of pencils. Find the original number of each.
Answers
no of pencils=y
x+y=60
=>y=60-x
Now let,x+25=3k
y-5=k
or,3(y-5)=3k
So,x+25=3(y-5)
or,x+25=3y-15
or,x+25=3(60-x)-15
or,x+25=180-3x-15
or,x+3x=180-15-25
or,4x=180-40
or,4x=140
or,x=140÷4
or,x=35
So,no of pens=35
no of pencils=60-35
=25
Concept
An approach to solving systems of equations known as substitution involves determining the value of one variable and then utilizing that value to determine the value of the other.
Given
total quantity of pens and pencils that Divya owns= 60
She has five fewer pencils and twenty-five more pens.
Find
We must ascertain how many pencils and pens she originally had.
Solution
let x represent number of pens and y represent the number of pencils.
therefore, total number of pens and pencils she have:
x ₊ y = 60 .......eq(1)
given, she has 25 more pens and 5 less pencils.
⇒ (x ₊ 25) ₊ (y ₋ 5) = 60
then the number of pens becomes 3 times the number of pencils.
⇒ 3y = x ....(2)
substituting 2 in eq(1) we get,
x ₊ y =60
3y ₊ y = 60
4y = 60
y = 60/4
y = 15
substitute y value in (2)
3y = x
3(15) = x
x = 45
Hence the number of pens and pencils Divya had is 45 and 15 respectively.
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