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
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Answers
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 = = 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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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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