Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $
10, and each wrench costs $6. If the solution region represents the number of hammers and wrenches that Brody can buy given his budget, determine which graph represents the solution set to the system of inequalities representing this situation.
2 answers:
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Answer:
x = 30 and x = 3 both solve the equation correctly. See work below.
Step-by-step explanation:
The very first step is to realize that p(x) is in hundreds of dollars and that the given number is not. 60000 is not in hundreds of dollars. It is in dollars. 60000 dollars = 60000/100 = 600 hundreds of dollars.
Make the polynomial = 600
-x^3+3x^2+900x-2100 = 600 Subtract 600 from both sides
-x^3+3x^2+900x-2100 - 600 = 0 Combine
-x^3+3x^2+900x- 2700 = 0 Group the first and second term and the Thrid and fourth terms.
(-x^2 + 3x^2) + (900x - 2700) = 0 Bring out the common factors from both groups.
-x^2(x - 3) + 900(x - 3) = 0 Factor out x - 3 on both sides of the plus sign
(- x^2 + 900)(x - 3) = 0 Reverse -x^2 + 900 to 900 - x^2
(900 - x^2)(x - 3) = 0 factor (900 - x^2) using the difference of squares
(30 - x)(30 + x) (x - 3) = 0
The two answers that work are
30 - x = 0 Solve
- x = - 30 Divide by - 1
-x/-1 = -30/-1 Combine
x = 30
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x - 3 = 0
x = 3
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There are two values that will work to give p(x) = 600. There is no way to account for why both values work.
The graph below confirms both answers.
