Maths-
General
Easy

Question

A ball pen costs Rs 3.50 more than pencil. Adding 3 ball pens and 2 pencils sum up to Rs 13. Taking y and z as costs of ball pen and pencil respectively. Write down 2 simultaneous equations in terms of y and z which satisfy the above statement. Find out the values of y and z.

Hint:

Taking y and z as costs of ball pen and pencil respectively
A ball pen costs Rs 3.50 more than pencil (i.e y = z + 3.50)
Adding 3 ball pens and 2 pencils sum up to Rs 13.(i.e 3y + 2z = 13)

The correct answer is: 4.00 rs


    Ans :- cost ball pen = 4.00 rs and cost of pencil  = 0.50 rs
    Explanation :-
    Taking y and z as costs of ball pen and pencil respectively
    L.e Cost of ball pen = y and cost of pencil = z
    Step 1:- form the system of linear equations using the given condition
    A ball pen costs Rs 3.50 more than pencil
    so, y = z + 3.50 —- Eq1
    Adding 3 ball pens and 2 pencils sum up to Rs 13.
    So, 3y + 2z = 13 —- Eq2
    We got Eq1 and Eq2 are simultaneous equations .
    Step 2:-  substitute the Eq1 in Eq2.
    3 y plus 2 z equals 13 not stretchy rightwards double arrow 3 left parenthesis z plus 3.50 right parenthesis plus 2 z equals 13
    not stretchy rightwards double arrow 3 z plus 2 z plus 10.50 equals 13
    not stretchy rightwards double arrow 5 z equals 2.50
    ∴ z = 0.50
    Step 3:-substitute the value of z in Eq1 to get the value of y
    y equals z plus 3.50 not stretchy rightwards double arrow y equals 0.50 plus 3.50 equals 4.00
    ∴ y = 4.00
    ∴ z = 0.50 rs is the cost of pencil and y = 4.00 rs is the cost of ball pen.

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