Question

6. Solve the following word problems:
a) The difference between two integers is 2. The larger integer is 6 less than twice the smaller. Find​

Answer 1

• Correct Question :-

Solve the following word problem:

a) The difference between two integers is 2. The larger integer is 6 less than twice the smaller. Find the integers.

• Given :-

Difference between two integers = 2

Larger Integer = 2(Smaller Integer) - 6

• Assumption :-

Let the smaller Integer be x

So,

Larger Integer = 2x - 6

• Solution :-

According to question,

Larger Integer - Smaller Integer = 2

⟹ 2x - 6 - x = 2

⟹ 2x - x - 6 = 2

⟹ x = 2 + 6

⟹ x = 8

So,

Smaller Integer = x = 8

Larger Integer = 2x - 6 = 2(8) - 6 = 16 - 6 = 10

• Verification :-

2x - 6 - x = 2

⟹ 10 - 8 = 2

⟹ 2 = 2

⟹ L.H.S = R.H.S

• Required Answer :-

The smaller and larger integers are 8 and 10 respectively.