Question

If ‘-’ means ‘+’, ‘+’ means ‘-’, ‘*’ means ‘‚’ and ‘‚’ means ‘*’ then which of the following will be the
correct equation?
a) 10 + 5 - 14 ÷ 10 * 15 = 158 b) 30 + 5 + 14 - 10 * 15 = 122
c) 30 - 5 + 14 ÷ 10 * 15 = 162 d) 30 * 5 - 4 ÷ 10 + 15 = 31

Answer 1

Step-by-step explanation:

$- \: \: means \: \: + \\ + \: \: means \: \: - \\× \: \: means \: \: ÷ \\ ÷ \: \: means \: \: × \\ \\ a) \: \: \: 10 + 5 - 14 ÷ 10 × 15 = 158 \\ \: \: \: \: 10 - 5 + 14 × 10 ÷ 15 = 158 \\ \: \: \: \: (10 - 5) + (14 \times \frac{ \cancel{10}_{ \: \: 2}}{ \cancel{15}_{ \: \: 3}} ) = 158 \\ \: \: \: \: 5 + \frac{28}{3} = 158 \\ \frac{15 + 28}{3} = 158 \\ \boxed{ \underline{ \underline{ \frac{43}{3} ≠ 158}}} \\ \\ b) \: \: \: 30 + 5 + 14 - 10 \times 15 = 122 \\ \: \: \: \: \: \: 30 - 5 - 14 + 10 \div 15 = 122 \\ \: \: \: \: (30 - 5 - 14) + (\frac{ \cancel{10}_{ \: \: 2}}{ \cancel{15}_{ \: \: 3}}) = 122 \\ 11 + \frac{2}{3} = 122 \\ \frac{33 + 2}{3} = 122 \\ \boxed{ \underline{ \underline{\frac{35}{3} ≠122}}} \\ \\ c) \: \: \: 30 - 5 + 14 ÷ 10 \times 15 = 162 \\ \: \: \: \: 30 + 5 - 14 \times 10 \div 15 = 162 \\ \: \: \: \: (30 + 5) - (14 \times \frac{ \cancel{10}_{ \: \: 2}}{ \cancel{15}_{ \: \: 3}} ) = 162 \\35 - \frac{28}{3} = 162 \\ \frac{105 - 28}{3} = 162 \\ \boxed{ \underline{ \underline{\frac{77}{3} ≠ 162}}} \\ \\ d) \: \: \: 30 \times 5 - 4 ÷ 10 + 15 = 31 \\ \: \: \: \: 30 \div 5 + 4 \times 10 - 15 = 31 \\ \: \: \: (30 \div 5) + (4 \times 10) - 15 = 31 \\ 6 + 40 - 15 = 31 \\ 46 - 15 = 31 \\ \boxed{ \underline{ \underline{31 = 31}}}$

Answer 2

Given:

For certain mathematical operations, if ‘-’ means ‘+’, ‘+’ means ‘-’, ‘*’ means ‘/’ and ‘/’ means ‘*’.

To Find:

Which of the following options is correct according to the above transformations.

a) 10 + 5 - 14 ÷ 10 * 15 = 158 b) 30 + 5 + 14 - 10 * 15 = 122

c) 30 - 5 + 14 ÷ 10 * 15 = 162 d) 30 * 5 - 4 ÷ 10 + 15 = 31

Solution:

Option a:

After transforming the signs as mentioned we get,

• 10 - 5 + 14 x 10 / 15,

=> 10 - 5 + 14 x (2/3),

=> 10 - 5 + 28/3,

=> 5 + 28/3,

=> 43/3. (The value doesnot match with the RHS value, hence it is incorrect).

Option b:

After transforming the signs as mentioned we get,

• 30 - 5 - 14 + 10 / 15,

=> 30 - 5 - 14 + 2/3,

=> 11 + 2/3,

=> 35/3. (The value doesnot match with the RHS value, hence it is incorrect).

Option c:

After transforming the signs as mentioned we get,

• 30 + 5 - 14 x 10 / 15,

=> 30 + 5 - 14 x 2/3,

=> 35 - 28/3,

=> 77/3.  (The value doesnot match with the RHS value, hence it is incorrect).

Option d:

After transforming the signs as mentioned we get,

• 30/5 + 4 x 10 - 15,

=> 6 + 4 x 10 -15,

=> 6 + 40 - 15 ,

=> 31. ( The value matches with the RHS value, hence it is the correct option).

Therefore, Option D is the correct answer.