Question

please tell this answer​

Answer 1

Step-by-step explanation:

a)if John had x marbles then gomathi had 45-x marbles

b)gomathi had 40-x marbles after losing 5 marbles

c) (x-5)(40-x)=124

40x-200-x²+5x=124

45x-x²=124+200

x²-45x+324

Answer 2

★ Concept

This question is based on Basic Algebra where the use of Algebraic Expression, linear equation in one variable and Quadratic Equation are common.

Let's proceed with calculation !!

$\rule{190pt}{1pt}$

Given that ::

John and Gomathi are playing with marbles such that all together they have 45 marbles.

a) If John had 'x' marbles, then how many marbles Gomathi had ?

Assumption made that John had 'x' marbles and it's already mentioned in the question that together John and Gomathi had 45 marbles.

→ John marbles + Gomathi marble = 45

→ Gomathi marbles = 45 - John marbles

→ Gomathi marbles = (45 - x) marbles.

Therefore, Gomathi had (45 - x) marbles.

b) How many marbles were left with Gomathi after losing 5 ?

Furthermore, it's given that both of them lost 5 marbles ; in previous sub part we have assumed John's marbles to be 'x' and so does Gomathi marbles came out to be (45 - x). After losing 5 marbles they were left with -

>> John's marbles = (x - 5)

Gomathi marbles = [(45 - x) - 5] = (40 - x)

Therefore, after losing 5 marbles Gomathi left with (40 - x) marbles.

c) Write an equation for the product of marbles they had after losing 5 marbles each.

Provided that, after losing 5 marbles each, the product of their marbles is 124 ; Mathematically

$\mapsto \sf(x - 5)(40 - x) = 124$

$\underline{\rule{190pt}{2pt}}$

Although in the question it's not mention to solve the equation further for 'x' (finding the number of marbles, they had originally). Here we go !! [Quadratic part using Factorisation]

$\mapsto \sf (x - 5)(40 - x) = 124$

$\mapsto \sf 40x - {x}^{2} - 200 + 5x = 124$

$\mapsto \sf {x}^{2} - 45x + 324 = 0$

$\mapsto \sf {x}^{2} - 36x - 9x + 324 = 0$

$\mapsto \sf \: x(x - 36) - 9(x - 36) = 0$

$\bf \: (x - 9)(x - 36) = 0$

Either

⋆ If (x - 9) = 0 ; x = 9

John had 9 marbles while Gomathi had (45 - 9) = 36 marbles.

⋆ If (x - 36) = 0 ; x = 36

John had 36 marbles while Gomathi had (45 - 36) = 9 marbles.