Question

A family has 560kg of rice for x number of weeks. If they need to use same amount of rice for 2 more weeks, they need to cut down their weekly consumption of rice by 5kgs. Find value of x.

Answer 1

Given :-

• A family has 560kg of rice for x number of weeks.
• If they need to use same amount of rice for 2 more weeks
• they need to cut down their weekly consumption of rice by 5kgs.

To Find :-

• Value of x ?

Solution :-

→ Original Consumption of Rice Per week = (560/x) kg.

→ New Weekly Consumption of Rice = 560/(x+2) kg.

Now, Given That, Difference b/w Original Consumption & New Consumption is 5kg.

So,

→ (560/x) - 560/(x+2) = 5

Taking LCM,

→ [ 560(x+2) - 560x ] /x(x+2) = 5

→ 560x + 1120 - 560x = 5x² + 10x

→ 5x² + 10x - 1120 = 0

→ 5(x² + 2x - 224) = 0

→ x² + 2x - 224 = 0

Splitting The Middle Term now,

→ x² - 14x + 16x - 224 = 0

→ x(x - 14) + 16(x - 14) = 0

→ (x - 14)(x + 16) = 0

→ X = 14 or (-16). [ Negative Value ≠ ]

Hence, Value of X is 14kg.

Answer 2

Question:

A family has 560kg of rice for x number of weeks. If they need to use same amount of rice for 2 more weeks, they need to cut down their weekly consumption of rice by 5kgs. Find value of x.

Answer:

Consumption of rice per week= 560/x...(1)

weekly consumption of rice= 560/x+2...(2)

Using (1) and (2)

$\implies \frac{560}{x} - \frac{560}{x + 2} = 5 \\ \\ \implies\frac{560(x + 2) - 560(x)}{x(x + 2)} = 5 \\ \\ \implies\frac{560x + 1120 - 560x}{ {2x + x}^{2} } = 5 \\ \\ \implies \: 560x + 1120 - 560x = 5({x}^{2} +2 x) \\ \\ \implies \: 560x + 1120 - 560x = {x}^{2} + 10x \\ \\ \implies \: 5 {x}^{2} + 10x - 1120 = 0 \\ \\ \implies \: {x}^{2} +2 x - 224 = 0 \\ \\ factorise \\ \\ {x}^{2} + 16x - 14x - 224 = 0 \\ \\ x(x + 16) - 14(x + 16) = 0 \\ \\ (x - 14)(x + 16) = 0$

$take \\ \\ x - 14 = 0 \: \: \: x + 16 = 0 \\ \\ x = 14 \: \: \: \: x = - 16$

we Ignore the negitive value of x=-16

Hence,

the value of x= 14kg.