Question 1121579: Mary’s age is at least five more than twice her brothers age. Is it possible for Mary to be 7? If Mary’s brother is 10 years old, how old is Mary?
I need to be able to model this scenario with an inequality and a visual representation of possible options. (Like graph it.)
This is a part of my summer homework and this is one of the few problems that I have left and I’m stuck.
I thought I could maybe use M (for Mary) and b (for Mary’s brother) in this equation to find out Mary’s age first off: M=2b+5
Besides that I’m stuck, I’ve gone to every possible website, but no other Algebra 2 word problems are similar to mine.
It would be amazing if you could help, if not hopefully I can figure it out XD. Thank you for reading this!
Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! brother is b
Mary is at least 2b+5 as you had, and that is M >=2b+5, greater than OR equal to, and that is "at least"
if brother is 10, Mary is at least 25, 2(10)+5. She may be older, but she has to be at least that.
The inequality is M >=+2b+5
Can Mary be 7? Then 7 >=2b+5
2 >= 2b
2b <= 2
b <= 1
Yes. She can be 7 if her brother is 1 or less than 1
Graphically, M >=2b +5. The area in quadrant 1 to be shaded (possible) can be determined by checking the origin. there, 0 >= 5, which is not true, so the upper part of the graph not involving the origin in Quadrant I represents the possibilities.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Your equation,  represents the youngest that Mary could be in relation to her brother's actual age. But you are given that Mary is at least five years older than twice her brother's age, so an inequality is required to correctly model the situation. So if the "equals" relationship is the youngest she can be, then she must either be equal to that age or greater, which is to say:
So what is  if  ?
And it certainly is possible for the brother to be one year old, and therefore it is, indeed, possible for Mary to be 7. In fact, if you don't restrict the domain of your inequality to the integers, Mary could be a good deal younger than 7 years old. Consider the situation where the brother was born 5 minutes ago. Then Mary could be as young as 5 years and 10 minutes old. Of course, you have no real idea about the upper bound of her age range except that there are practical limitations on the difference in ages of a given woman's oldest and youngest child. For Mary to be 30 years older than her brother in the real world would be quite a stretch for their mother.
As to Mary's age when the brother is 10, just plug 10 into your inequality and do the indicated arithmetic:
\ +\ 5)
John
My calculator said it, I believe it, that settles it
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