The difference of two numbers is 6.if five times the smaller number is 2 more than four times the larger number, find the two numbers

Answer 1

Let x = smaller number and let y = larger number.

Then translate the words into mathematical language: y - x = 6 and 5x = 4y + 2.

Since y - x = 6, so y = x + 6. Substitute x + 6 for y in the second equation: 5x = 4(x + 6) + 2.

Then 5x = 4x + 24 + 2 and x = 26. Finally, find y = 26 + 6 = 32.

Check that the difference is 6 and that 5*26 = 4*32 + 2.

Answer 2

The difference of 2 numbers is 6, means we dont know what the 2 numbers are, so i will give the first number (x) and the second number (y).

x - y = 6 (this means y is smaller than x since the result is a positive 6 . This is (EQUATION 1)

"if five times the smaller number is 2 more than four times the larger number"

Then think of 5y = 4x + 2

Solve for y:

y = (4x +2) / 5 (EQUATION 2)

Substitute y = (4x +2) / 5 in the first equation x - y = 6

x - (4x + 2) / 5 = 6

5x / 5 - (4x + 2) / 5 = 6

(5x - 4x - 2) / 5 = 6 cross multiply

x - 2 = 5 x 6

x -2 = 30

x = 32

Substitute x = 32 on the second equation

y = 4(32) + 2 / 5

y = 130 / 5

y = 26

Check:

x - y = 6

32 - 26 = 6

6 = 6