Question

a bag and an umbrella cost 500 rs the price of the bag is 150rs. more than that of umbrella. find the price of each one ? explain the method you found out in algebraic expression
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Answer 1

Answer:-

$\red{\bigstar}$ Cost of

Bat $\large\leadsto\boxed{\tt\purple{Rs. 325}}$

Umbrella $\large\leadsto\boxed{\tt\purple{Rs. 175}}$

• Given:-

Price of bat and umbrella is Rs. 500

Cost of the bat is Rs. 150 more than that of umbrella

• To Find:-

Cost of bat and umbrella.

• Solution:-

Let the cost of the bat be 'x' and cost of the umbrella be 'y'.

• According to the question:-

Price of bat and umbrella is Rs. 500

Therefore,

$\pink{\bigstar}$ $\bf{x + y = 500} \dashrightarrow\bf\red{[eqn.i]}$

Also,

The cost of bat is Rs. 150 more than that of umbrella.

We know, Cost of umbrella is y and of bat is x.

Hence,

$\pink{\bigstar}$ $\bf{x = y+150} \dashrightarrow\bf\red{[eqn.ii]}$

• Substituting the eqn.[ii] in eqn.[i]:-

→ $\sf x+y = 500$

→ $\sf y+150 + y = 500$

→ $\sf 2y + 150 = 500$

→ $\sf 2y = 500-150$

→ $\sf 2y = 350$

→ $\sf y = \dfrac{350}{2}$

$\pink{\bigstar}$ $\large{\tt\blue{y = 175}}$

• Substituting the value of y in eqn.[i]:-

→ $\sf x + y = 500$

→ $\sf x + 175 = 500$

→ $\sf x = 500 - 175$

$\pink{\bigstar}$ $\large{\tt\blue{x = 325}}$

Therefore, the cost of bat is Rs. 325 and the cost of umbrella is Rs. 175.

$\red{\bigstar}$ Verification:-

→ $\sf 175 + 325$

→ $\sf 500$

★ HENCE VERIFIED★