About Chanda Walker Expertise I can answer word problems involving mathematics at the high school and college level. I particularly enjoy calculus word problems. Please don't just type the math problem without comments. If you don't tell me what problem your having, I can't help.
Experience Have done word problems as a tutor and as a student of mathematics and physics for years.
Organizations Sigma Xi
Education/Credentials Optical Science PhD
Past/Present Clients I've answered hundreds of questions here at AllExperts.com in algebra, physics and general math sections.
Word Problems - High school word problem involving inequalities
Expert: Chanda Walker - 4/29/2009
Question QUESTION: Hi, this is my question:
The age of the youngest of three sisters is 7 years less than twice the age of the middle sister. The oldest sister is 11 years older than twice the age of the youngest sister. If the sum of their ages is more than 20, what are the lowest possible ages of the sisters.
The ages must be full units, eg. one sister's age can't be 8.5 yrs, all 3 ages must be full units.
I don't really know which sister i should place as x, i'm kind of switching from the youngest and the middle.
I'd really appreciate if you could solve the problem for me using inequalities, also if you could show me the working out. I found the answer, but it was not a full unit, (youngest sis was like 1.452... yrs old). I would also find it really helpful if you could show working out.
Thanks very much!
ANSWER: youngest = x
x = 2(middle) - 7
2x + 11 = oldest
Solve for the age of the middle in terms of x . . .
The youngest sister can be 11/7 or 1.571 years old.
The middle would then be 30/7 or 4.286.
The oldest would be 99/7 or 14.143.
Let me know if I can help further.
---------- FOLLOW-UP ----------
QUESTION: Hi again. I was asking that the answer would be in full units, as advised by the question. Also, according to the answers the answer is 3, 5, 17. All i need to know is how to get the answer using inequalities.
Thanks for the help.
Answer I showed you how to solve using inequalities. Here is the work.
x + (x + 7)/2 + 2x + 11 >20
7/2 x + 14.5 >20
7/2 x > 5.5
7x > 11
x > 11/7
Since we know the youngest is greater than 1.5 one might round her age up to 1. But her age has to be an odd number since she is 7 years less than an even number (2 times the age of the middle sister is always going to be an even number). The youngest has to be 3.
Knowing the youngest is 3, then the middle must be 5. And the oldest must be 17.
