Quote:
The cost of 3 chocolates, 5 biscuits, and 5 ice creams is 195. What is the cost of 7 chocolates, 11 biscuits and 9 ice creams?
(1) The cost of 5 chocolates, 7 biscuits and 3 ice creams is 217.
(2) The cost of 4 chocolates, 1 biscuit and 3 ice creams is 141
If \(3c+5b+5i=195\), what is the value of \(7c+11b+9i\)?
Statement 1: \(5c+7b+3i=217\)Multiplying \(3c+5b+5i=195\) by 3, we get:
\(9c+15b+15i=585\)
Adding together \(9c+15b+15i=585\) and \(5c+7b+3i=217\), we get:
\(14c+22b+18i=802\)
\(7c+11b+9i=401\)
SUFFICIENT.
Statement 2: \(4c+b+3i=141\)Adding together \(3c+5b+5i=195\) and \(4c+b+3i=141\), we get:
\(7c+6b+8i=336\)
No way to determine the value of \(7c+11b+9i\).
INSUFFICIENT.
One way to prove that S2 is INSUFFICIENT:
Case 1: c=15
Statement 2 equation --> \(4*15+b+3i=141\) --> \(b+3i=81\)
Prompt equation --> \(3*15+5b+5i=195\) --> \(5b+5i=150\) --> \(b+i=30\)
Subtracting the prompt equation from the Statement 2 equation, we get:
\(2i=51\)
\(i=25.5\)
Since \(b+i=30\), \(b=4.5\)
In this case, \(7c+11b+9i=(7*15)+(11*4.5)+(9*25.5)=105+49.5+229.5=384\)
Case 1: c=25
Statement 2 equation --> \(4*25+b+3i=141\) --> \(b+3i=41\)
Prompt equation --> \(3*25+5b+5i=195\) --> \(5b+5i=120\) --> \(b+i=24\)
Subtracting the prompt equation from the Statement 2 equation, we get:
\(2i=17\)
\(i=8.5\)
Since \(b+i=24\), \(b=15.5\)
In this case, \(7c+11b+9i=(7*25)+(11*15.5)+(9*8.5)=175+170.5+76.5=422\)
Since \(7c+11b+9i\) can be different values, INSUFFICIENT.