Solve these word problems by graphing, substitution or elimination.

(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.

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