Question

The difference between two integers is 2. The larger integer is 6 less than twice the smaller. Find the integers.
THE OPTIONS ARE:
1 and 3

2 and 4

8and 10

none of the above​

Answer 1

The integers are 8 and 10.

Option c is right.

CONSIDER:

• Let the two integers be x and y.

• Let x be the smaller integer.

• Let y be the larger integer.

GIVEN:

• The difference between two integers is 2.
• y - x = 2

• The larger integer is 6 less than twice the smaller.
• y = 2x - 6

TO FIND:

The smaller and larger integer, x and y

SOLUTION:

Consider the equation, y - x = 2

$y - x = 2 \\ \\ y = 2 + x$

Substitute y = 2 + x in the equation y = 2x - 6

$y = 2x - 6 \\ \\ 2 + x = 2x - 6 \\ \\ 2 + 6 = 2x - x \\ \\ 8 = x \\ \\ x = 8$

The smaller integer is 8.

Substitute x = 8 in the equation y - x = 2

$y - x = 2 \\ \\ y - 8 = 2 \\ \\ y = 2 + 8 \\ \\ y = 10$

The larger integer is 10.

ANSWER:

• The smaller integer is 8.

• The larger integer is 10.