SOLUTION: I have 2 problems I need help, but it's quadratic equations word problems. SERIOUSLY!! Problem 1: Jim has a photo measuring 8 by 6 cm. He wants to half the area of the original p

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I have 2 problems I need help, but it's quadratic equations word problems. SERIOUSLY!! Problem 1: Jim has a photo measuring 8 by 6 cm. He wants to half the area of the original p      Log On


   

Question 884542: I have 2 problems I need help, but it's quadratic equations word problems. SERIOUSLY!!
Problem 1:
Jim has a photo measuring 8 by 6 cm. He wants to half the area of the original photo by reducing the length and width by the same amount. What are the new dimensions of the photo?
Problem 2:
Bill mows a lawn measuring 100 by 120 feet. He mows only one-third of the lawn by mowing a strip of uniform around the outer edge of the lawn. What is the width of the strip?
Found 3 solutions by josgarithmetic, geetha_rama, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Question 1 is not clear but two choices are possible for what you mean. Question 2 is a little complicated but a good exercise. I will help with question 2.

The uniform width strip is some x feet wide. The entire lawn is 100%2A120 square feet, but the unmowed part will be %28100-2x%29%28120-2x%29.

The area of the mowed strip is 100%2A120-%28100-2x%29%28120-2x%29; and the problem description tells you that this is %281%2F3%29%28100%2A120%29 square feet. This means in numbers, highlight_green%28100%2A120-%28100-2x%29%28120-2x%29=%281%2F3%29100%2A120%29.
-
The rest of the process is algebraic steps. You want to simplify and solve for x, the uniform width.

100%2A120-100%2A120-240x-200x%2B4x%5E2=%281%2F3%29100%2A120
-440x%2B4x%5E2=%281%2F3%29100%2A120
4x%5E2-440x-%281%2F3%29100%2A120=0
x%5E2-110x-%281%2F3%2925%2A120=0
x%5E2-110x-25%2A40=0
highlight_green%28x%5E2-110x-1000=0%29
-
Check the discriminant: %28-110%29%5E2-4%2A%28-1000%29=16100=7%2A23%2A100.
General Solution:
x=%28110%2B-+sqrt%287%2A23%2A100%29%29%2F2
x=%28110%2B-+10sqrt%28161%29%29%2F2
highlight%28x=55%2B5sqrt%28161%29%29, in FEET. You must use the PLUS form of solution.

Answer by geetha_rama(94) About Me  (Show Source):
You can put this solution on YOUR website!
Pbm 1:
Let x be the amount of width to be reduced from the original dimension
Area of the new photo
%288-x%29%2A%286-x%29=24
x%5E2-14x%2B48=24
x%5E2-14x-24=0
Roots of the quadratic eqn %28-b%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29
Solving, %2814%2B-sqrt%2814%5E2-4%2A24%29%29%2F2
Solve the above and we get Roots as 12, 2
Hence we need to reduce the original photo by 2cm.
New dimensions are 6cm * 4 cm
Pbm 2:
Let the width of the strip be x feet
Original area - (area not mowed) = area mowed
12000+-+%28120-x%29%2A%28100-x%29+=+%281%2F3%29%2A12000
-x%5E2+%2B+220%2Ax+=+4000+
x%5E2-220%2Ax-4000
Solving for the roots of the quad eqn using the above mentioned formula we get roots as 20, 200
Hence width of the strip = 20 feet

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
I have 2 problems I need help, but it's quadratic equations word problems. SERIOUSLY!!
Problem 1:
Jim has a photo measuring 8 by 6 cm. He wants to half the area of the original photo by reducing the length and width by the same amount. What are the new dimensions of the photo?
Problem 2:
Bill mows a lawn measuring 100 by 120 feet. He mows only one-third of the lawn by mowing a strip of uniform around the outer edge of the lawn. What is the width of the strip?


No 1.

New dimensions: highlight_green%28highlight_green%286cm_by_4cm%29%29 

No. 2

Width of mowed section: highlight_green%28highlight_green%2810ft%29%29   

You can do the check!! 



If you need a complete and detailed solution, let me know!!



Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.

Further help is available, online or in-person, for a fee, obviously. 



For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams,GENERAL

MATH and HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra, 

Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE,

GRE, CLEP, and the TASC/GED, you can visit: http://asvabstudyzone.freeforums.net/.