Question

A washer and a dryer cost $959 combined. The washer costs $59 more than the dryer. What is the cost of the dryer?

Answer 1

$450

Explanation:

1. First, let's make a system of equations:

• 
  `y+59=x,x+y=959` (y = dryer, x = washer)

2. (Solving)

Solve y + 59 = x for y:

• 
  `y + 59 = x`
• 
  `y + 59-59=x-59` (Subtract 59 from both sides)
• 
  `y = x-59`

Substitute x - 59 for y in x + y = 959

• 
  `x + y = 959`
• 
  `x+x-59=959`
• 
  `2x - 59 = 959`
• 
  `2x - 59 + 59 = 959 + 59` (Add 59 to both sides)
• 
  `2x = 1018`
• 
  `(2x)/(2) = (1018)/(2)` (divide both sides by 2)
• 
  `x = 509`

Substitute 509 for x in y = x - 59

• 
  `y = x - 59`
• 
  `y = 509-59`
• 
  `y = 450`

Therefore, the dryer costs $450. (The washer costs $509).

Answer 2

A dryer costs $450.

A washer costs $509.

Explanation:

Let:

"washer" = x

"dryer" = y

Set the equations:

x + y = 959

x = y + 59

First, plug in y + 59 for x in the first equation for x:

x + y = 959

(y + 59) + y = 959

Simplify, combine like terms:

y + y + 59 = 959

2y + 59 = 959

Next, isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis, Exponents (& Roots), Multiplications, Divisions, Additions, Subtractions.

First, subtract 59 from both sides of the equation:

2y + 59 (-59) = 959 (-59)

2y = 959 - 59

2y = 900

Next, divide 2 from both sides of the equation:

(2y)/2 = (900)/2

y = 900/2

y = 450

Next, plug in 450 for y in one of the equations:

x = y + 59

x = (450) + 59

x = 509

Check:

x + y = 959

450 + 509 = 959

959 = 959 (True).

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