Math, asked by eshalfarah123, 8 months ago

School authorities of two schools A and B decided to honour the values of honesty and

empathy among their students. School A awarded 5 prizes for honesty and 3 prizes for

empathy whereas school B awarded 3 prizes for honesty and 5 prizes for empathy, the

cost of prizes being same for both schools. If schools A and B spent ₹ 3700 and ₹ 3500

respectively, find the price of each prize given for honesty and each prize given for

empathy.

with steps pls...fast

will mark as brainliest

Answers

Answered by bhagyashreechowdhury
3

Given:

School A awarded 5 prizes for honesty and 3 prizes for  empathy

School B awarded 3 prizes for honesty and 5 prizes for empathy

Schools A and B spent ₹ 3700 and ₹ 3500  respectively

To find:

The price of each prize given for honesty and each prize given for  empathy.

Solution:

Let's assume,

"h" → represent the price of each prize given for honesty

"e" → represent the price of each prize given for empathy

Now, according to the question, we can form two linear equations as,

Expenditure by School A:

5h + 3e = 3700 .......  (i)

Expenditure by School B:

3h + 5e = 3500 ....... (ii)

Multiplying eq. (i) by 3 and eq. (ii) by 5, we get the equations as,

15h + 9e = 11100 .......  (iii)

15h + 25e = 17500 ....... (iv)

Subtracting eq. (iii) from eq. (iv), we get

15h + 25e = 17500

15h + 9e = 11100

-       -         -

------------------------------

        16e = 6400

------------------------------

e = \frac{6400}{16} = 400

Substituting e = 400 in eq. (i), we get

5h + (3×400) = 3700

⇒ 5h = 3700 - 1200

⇒ 5h = 2500

h = 500

Thus,

The price of each prize given for honesty is ₹ 500.

The price of each prize given for  empathy is ₹ 400.

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Answered by amitnrw
0

Given :  School A awarded 5 prizes for honesty and 3 prizes for empathy whereas school B awarded 3 prizes for honesty and 5 prizes for empathy.  schools A and B spent ₹ 3700 and ₹ 3500 respectively  

To find : price of each prize given for honesty and each prize given for empathy.

Solution:

Cost for Honesty  prize =  A  ₹

Cost for Empathy prize = B   ₹

School A awarded 5 prizes for honesty and 3 prizes for empathy

=> 5A  + 3B  = 3700    Eq1

school B awarded 3 prizes for honesty and 5 prizes for empathy

=> 3A  + 5B  = 3500    Eq2

Adding both

=> 8A + 8B = 7200

=> A + B = 900    Eq3

Eq1 - Eq2

=> 2A - 2B = 200

=> A - B  = 100    Eq4

Eq3 + Eq4

=> 2A  = 100

=> A = 500   => B = 400

price of each prize given for honesty  = 500  ₹

price of each prize given for empathy  = 400  ₹

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