SOLUTION: 1. The average of three consecutive even numbers is more than 100. Find the smallest set of numbers. --write an expression representing the sum of three consecutive even numbers

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Question 152126This question is from textbook Algebra and Trigonomety
: 1. The average of three consecutive even numbers is more than 100. Find the smallest set of numbers.
--write an expression representing the sum of three consecutive even numbers.
--write the expression representing the average of the three consecutive even numbers.
--write the inequality to solve the problem.
--solve the problem and answer the question.
2.The sides of an equilateral is increased by 5,10, and 15. if the perimeter of the new triangle is more than twice the original triangle, what could be the length of the equilateral triangle?
--draw a digram of the two triangles.
--write an expression for the perimeter of the equilateral triangle.
--write an expression for the perimeter of the new triangle.
--write the inequality to solve the problem.
--solve the inequality and answer the question.
3.Joey is building a larger kennel for his dog. His dog's kennel is currently 4'x6'. he increases the length and width by the same amount. if the perimeter of the new kennel is at most twice the perimeter of the original kennel, how much could he increase the length and width of the old kennel?
--draw a diagram of the problem:
--write an expression representing the perimeter fo the new kennel:
--write the inequality to solve the problem:
--solve the problem and answer the question. This question is from textbook Algebra and Trigonomety

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1. The average of three consecutive even numbers is more than 100. Find the smallest set of numbers.
:
--write an expression representing the sum of three consecutive even numbers.
x + (x+2) + (x+4)
3x + 6
;
--write the expression representing the average of the three consecutive even numbers.
%283x+%2B+6%29%2F3
:
--write the inequality to solve the problem.
%283x+%2B+6%29%2F3 > 100
:
--solve the problem and answer the question.
%283x+%2B+6%29%2F3 > 100
Multiply both sides by 3:
3x + 6 > 300
3x > 300 - 6
3x > 294
x > 294%2F3
x > 98
Min values for 3 consecutive even no. > 100 = 100, 102, 104
:
2.The sides of an equilateral is increased by 5,10, and 15. if the perimeter of the new triangle is more than twice the original triangle, what could be the length of the equilateral triangle?
:
--draw a digram of the two triangles. You will have to do that
:
--write an expression for the perimeter of the equilateral triangle.
3s
:
--write an expression for the perimeter of the new triangle.
(s+5) + (s+10) + (s+15)
3s + 30
:
--write the inequality to solve the problem.
3s + 30 > 2(3s)
3s + 30 > 6s
3s - 6s > -30
-3s > -30
Get rid of the neg, mult eq by -1, this reverses the inequality sign
3s < 30
s < 30%2F3
s < 10
:
--solve the inequality and answer the question.
The greatest integer value for s would have to = 9 (length of equilateral tri.)
:
:
3.Joey is building a larger kennel for his dog. His dog's kennel is currently 4'x6'. he increases the length and width by the same amount. if the perimeter of the new kennel is at most twice the perimeter of the original kennel, how much could he increase the length and width of the old kennel?
:
Let x = amt of increase
:
--draw a diagram of the problem:
:
--write an expression representing the perimeter of the new kennel:
2(x+4) + 2(x+6)
2x + 8 + 2x + 12
4x + 20
:
--write the inequality to solve the problem:
4x + 20 =< 2[2(4) + 2(6)]
4x + 20 =< 2[8 + 12]
4x + 20 =< 2(20)
4x + 20 =< 40
4x =< 40 - 20
4x =< 20
x =< 20%2F4
x =< 5 ft, max increase of dimensions