Question

plzz help.......... ​

Answer 1

Answer :-

$\: \: \underline{\boxed{\sf{\purple{Let's \: understand \: to \: the \: voice \: of \: question\: (Analysis)}}}}$

Here we see that we are needed to find two different values. We can find them using Linear Equations in Two Variables. Then we can make tue value of both unknown values depend on other to find them both. Let's do this question, using this concept.

_____________________________________

⭐ Question :-

The ratio of the rose plants to marigold plants in an orchard is 2:3. If 5 more plants of each type are planted, the ratio of plants would be 5:7. Then find the number of rose plants and marigold plants in the orchard.

_____________________________________

⭐ Solution :-

Given,

» Number of rose plant : Number of Marigold Plant = 2:3

» 5 + Number of Rose Plant : 5 + Number of Marigold Plant = 5 : 7

• Let the number of rose plant be 'x'.

• Let the number of Marigold plant be 'y'.

The according to the question,

——:: Case I :-

$\: \: \huge{\orange{\longrightarrow \: \: \dfrac{x}{y} \: = \: \dfrac{2}{3}}}$

By cross multiplication, we get,

➔ 3x = 2y

➔ y = ½ × (3x) ....(i)

——:: Case II :-

$\: \: \huge{\orange{\longrightarrow \: \: \: \dfrac{x \: + \: 5}{y \: + \: 5} \: = \: \dfrac{5}{7}}}$

By cross multiplication, we get,

➔ 7(x + 5) = 5(y + 5)

➔ 7x + 35 = 5y + 25

➔ 7x - 5y = 25 - 35

➔ 7x - 5y = -10 ...(ii)

From equation, (i) and (ii), we get,

↬ 7x - (5 × ½ × 3x) = -10

Multiplying all the terms by 2 , at each side, we get,

↬ 14x - 15x = -20

↬ -x = -20

Cancelling the negative sign, we get,

↬ x = 20

• Hence, the number of rose plants = x = 20.

From equation (i) and value of x, we get,

↬ y = ½ × 3x

↬ y = ½ × 3(20)

↬ y = ½ × 60 = 30

• Hence the number of Marigold plants = y = 30

$\: \: \underline{\boxed{\sf{\green{Thus, \: the \: number \: of \: rose \: plants \: are \: \underline{20} \: and \: that \: of \: marigold \: are \: \underline{30}}}}}$

________________________________

$\: \: \mapsto \: \: \underline{\rm{\blue{Confused ? \: Don't \: worry \: let's \: verify \: it}}}$

For verification, we need to simply apply the values we got, into our equations.

~ Case I :-

✰ y = ½ (3x)

✰ 30 = ½(3(20))

✰ 30 = ½(60)

✰ 30 = 30

Clearly, LHS = RHS.

~ Case II :-

✰ 7x - 5y = -10

✰ 7(20) - 5(30) = -10

✰ 140 - 150 = -10

✰ -10 = -10

Clearly LHS = RHS

Here both the conditions satisfy, so our answer is correct.

HENCE, VERIFIED.

_______________________________

$\: \: \huge{\mapsto \: \:\underline{\sf{\red{More \: to \: know \: :-}}}}$

• Linear Equations are the equations formed using variables and constanta of single degrees.

• Polynomials are the equations formed using constant and variables of multiple degrees.

• Polynomials are of different types :-

Linear Polynomial

Quadratic Polynomial

Cubic Polynomial

Bi - Quadratic Polynomial

• Linear Equations are of three types :-

Linear Equation In one Variable

Linear Equation in Two Variables

Linear Equation in Three Variables

Answer 2

Answer:

Let the number of rose plants be

′

x

′

the number of marigold plants=2×x+5

=2x+5.

given number of marigold plants 15

⇒ 2x+5=15

⇒ 2x=10

⇒ x=5

∴ There are 5 rose plants.