Nicole bought a bag containing assorted hard candies from the local corner store. They were on clearance and she got a good deal
1 answer:
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Answer:
n = 14
Step-by-step explanation:
Write the equation in algebraic (numbers and symbols) form
= n + 3 Rearrange the equation
= n(n + 3) Multiply both sides by 'n'
238 = n(n + 3) On the left, multiplying and dividing by 'n' cancels out
238 = n² + 3n Distributed right side
0 = n² + 3n - 238 Rearranged to standard form for quadratic equations
Remember standard form for quadratic equations is: ax² + bx + c = 0
State the variables a, b and c:
a = 1; b = 3; c = -238
When a quadratic equation is in standard form, you can <u>use the quadratic formula</u> to solve for 'n'. (Usually, you see the variable 'x', but the quadratic formula can solve for 'n' as if it is 'x', as long as it's in standard form.)
(ignore the Â, it's a formatting error)
Substitute the values for 'a', 'b' and 'c' from the equation
In the root, two negatives make a positive
Add inside the root
Find the square root of 961
Split the equation at the ±
Split for adding:
Simplify
n = 14
Split for subtracting:
Simplify
n = -17
You get the answers 14 and -17 for 'n'. Decide which one is 'inadmissible', meaning it can't be right even if it solves the equation.
The problem says 'n' is a natural number. <u>Natural numbers are all non-partial numbers count up from 1.</u> (Non-partial means as a fraction, they are reduced to a number over 1). Since -17 is less than 1, it is inadmissible because it is not a natural number.
Therefore, 'n' is 14.