(1) The numbers are 8 and 16.
(2) John have 12 nickels and 6 dimes.
Solution:
(1) Let x and y be the two numbers.
Sum of two numbers = 24
⇒ x + y = 24 – – – – (1)
One number = Other number – 8
⇒ x = y – 8 – – – – (2)
Substitute equation (2) in equation (1), we get
⇒ y – 8 + y = 24
⇒ 2y – 8 = 24
Add 8 on both side of the equation, we get
⇒ 2y = 32
Divide by 2 on both sides.
⇒ y = 16
Substitute y = 16 in equation (2)
⇒ x = 16 – 8
⇒ x = 8
Hence the numbers are 8 and 16.
(2) Let n and d be the nickels and dimes respectively.
Nickels + Dimes = 18
⇒ n + d = 18 – – – – (1)
Nickles = Dimes + 6
⇒ n = d + 6 – – – – (2)
Substitute equation (2) in equation (1), we get
⇒ d + 6 + d = 18
⇒ 2d + 6 = 18
Subtract 6 from both side of the equation.
⇒ 2d = 12
Divide by 2 on both side of the equation, we get
⇒ d = 6
Substitute d = 6 in equation (1), we get
⇒ n = 6 + 6
⇒ n = 12
Hence John have 12 nickels and 6 dimes.
