Three slogans were finalized and the number of banners made for each slogan is in A.P. If the total number of banners made is 90 and their product is 5130, then find the no. of banners for each type of slogan. (a) 7, 50, 33 (b) 3, 30, 57 (c) 5, 53, 32 (d) 7, 50, 30
Answers
Given : Three slogans were finalized and the number of banners made for each slogan is in A.P.
the total number of banners made is 90 and their product is 5130,
To find : the no. of banners for each type of slogan.
(a) 7, 50, 33 (b) 3, 30, 57 (c) 5, 53, 32 (d) 7, 50, 30
Solution:
let say number of banners are
a - d , a , a + d
Sum = a - d + a + a + d = 3a = 90
=> a = 30
Hence banners are
(30 - d) , 30 , (30 + d)
Product is 5130
=> (30 - d)(30) (30 + d) = 5130
=> 900 - d² = 171
=> d² = 729
=> d = 27
30 - d = 30 - 27 = 3
30 + d = 30 + 27 = 57
hence numbers are 3 , 30 , 57
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Question :- Three slogans were finalized and the number of banners made for each slogan is in A.P. If the total number of banners made is 90 and their product is 5130, then find the no. of banners for each type of slogan.
(a) 7, 50, 33
(b) 3, 30, 57
(c) 5, 53, 32
(d) 7, 50, 30
Answer :-
Let three banners are (a - d), a and (a + d) .
so,
→ (a - d) + a + (a + d) = 90
→ 3a = 90
→ a = 30 .
then,
→ (30 - d) * 30 * (30 + d) = 5130
→ (30² - d²) = 5130/30
→ 900 - d² = 171
→ d² = 900 - 171
→ d² = 729
→ d = ±27
taking d = 27,
a - d = 30 - 27 = 3
a = 30
a + d = 30 + 27 = 57 .
therefore, option (b) is correct .
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