Question

Four tenths of a number increased by the second number equals 19. One tenth of the first number decreased by the second number is equal to 1. What are the two numbers?

Answer 1

The two numbers are 40 and 3

Explanation:

Assume that the first number is x and the second number is y

∵ Four tenths =
`(4)/(10)` = 0.4

∵ One tenth =
`(1)/(10)` = 0.1

∵ Four tenths of 1st number increased by the 2nd number equals 19

∵ The 1st number = x and the 2nd number = y

∴ 0.4x + y = 19 ⇒ (1)

∵ One tenth of the 1st number decreased by the 2nd number is equal to 1

∴ 0.1x - y = 1 ⇒ (2)

Now we have a system of equations to solve it

→ Add equations (1) and (2) to eliminate y

∵ (0.4x + 0.1x) + (y + -y) = (19 + 1)

∴ 0.5x + 0 = 20

∴ 0.5x = 20

→ Divide both sides by 0.5 to find x

∵
`(0.5x)/(0.5)` =
`(20)/(0.5)`

∴ x = 40

→ Substitute the value of x in equation (1) or (2) to find y

∵ 0.4(40) + y = 19

∴ 16 + y = 19

→ Subtract 16 from both sides

∴ 16 - 16 + y = 19 - 16

∴ y = 3

∴ The two numbers are 40 and 3