Question

The sum of two nos. is 82. The larger number exceeds three times the smaller one by 6.
Find the numbers
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Answer 1

★GIVEN★

The sum of two nos. is 82. The larger number exceeds three times the smaller one by 6.

★To Find★

Find the numbers.

★SOLUTION★

• Let the smaller number be x
• Let the larger number be 3x+6
• Sum is 82

According to the question,

=> x + 3x + 6 = 82

=> 4x + 6 = 82

=> 4x = 82 - 6

=> x = 76/4

=> x = 19

The numbers are:-

1. x = 19
2. 3x + 6 = 3 × 19 + 6 = 63

★VERIFICATION★

=> 63 + 19 = 82

=> 82 = 82

=> LHS = RHS

The numbers are 19 and 63.

Answer 2

★GIVEN★

The sum of two nos. is 82. The larger number exceeds three times the smaller one by 6.

★To Find★

The numbers.

★SOLUTION★

1. Let the smaller number be x.
2. Let the greater number be 3x + 6.
3. Sum = 82.

According to the question,

$\large\implies{\sf{x+3x+6=82}}$

$\large\implies{\sf{4x+6=82}}$

$\large\implies{\sf{4x=82-6}}$

$\large\implies{\sf{4x=76}}$

$\large\implies{\sf{x=\dfrac{76}{4}}}$

$\large\implies{\sf{x=\dfrac{\cancel{76}}{\cancel{4}}}}$

$\large\therefore\boxed{\bf{x=19}}$

The numbers are:-

1. x = 19
2. 3x + 6 = 3 × 19 + 6 = 57 + 6 = 63

★VERIFICATION★

$\large\implies{\sf{19+63=82}}$

$\large\implies{\sf{82=82}}$

$\large\therefore\boxed{\bf{LHS=RHS}}$

The numbers are 19 and 63.