Maths homework - inequality

Discussion in 'General Discussion' started by Tahir2, Jan 14, 2018.

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1. Tahir2 Veteran

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Hey there

Trying to help my daughter with some math homework.

Pam is 7 years younger than Amanda. Amanda is u years old.
a) write an expression for Pam's age.
b) Pam is 16 years old or older. Show this as an inequality.
c) Solve this to show an inequality for Amanda's age.

What I have is:

a) 7 - u > p
b) 16p > 7 - u
c)) 23 >

???
And another one...

Tim is half Jill's age, Jill is b years.
a) write an expression for Jill's age.
b) Tim is 14 years old or younger, show this as an inequality.
c) Show an inequality for Jill's age.

Never done these before, am I even on the right track....

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2. BRiT (>• •)>⌐■-■ (⌐■-■) ModeratorLegendAlpha

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Here's how I'm initially parsing things. The first expression A is an exact statement, not an inequality. For statement B you use substitution for pam's age (p) in relations to Amanda's (u -7).

a) u - 7 = p
b) p >= 16
u - 7 >= 16

c) u - 7 >= 16
u >= 16 + 7
u >= 23

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3. Tahir2 Veteran

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It is an inequality as Pam is 16 years old or older. Or so I thought.

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4. BRiT (>• •)>⌐■-■ (⌐■-■) ModeratorLegendAlpha

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For the second part my logic after only 4 hours of sleep { big ole disclaimer, so look for obvious mistakes, but here's how I processed it with logic } ...

[ we use t for Tim's age and j for Jill's age ]
t = 1/2 j
[ multiply both sides by 2 to normalize for j ]
2 * t = j
[ now we use 'b' for jills age ]
2 * t = b
[ written for b as base statement on left side]
b = 2 * t

a) b = 2 * t
b) t <= 14
c) b <= 2 * t
b <= 2 * 14
b <= 28

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5. BRiT (>• •)>⌐■-■ (⌐■-■) ModeratorLegendAlpha

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Yes, but that doesn't come into play until step C.
I took it one statement at a time and worked with that.

"Pam is 7 years younger than Amanda."
p = Amanda - 7

Next we plug in the second statement: "Amanda is u years old."
p = u - 7.

Of course, many people can apply things in different orders, and this is just how I processed it.

I added more step descriptions in my second response for the next part.

Hope this helps, as I know it's really rough having to help children with homework as they likely change the way they want them to work or show their work. Despite nearly having a BS in Applied Mathematics (almost double major to go with my BS in Comp.Sci) I can't even help my 7 year old niece on her homework because of "Common Core" methods in the US.

It's rough, but hang in there and talk with them to try to reason it out. I find it far better to have them understand the steps of problem solving than it is to force a specific method on them.

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6. Silent_Buddha Legend

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There are many ways to represent things.

Pam is 7 years younger than Amanda.
1. Pam = Amanda - 7
2. Pam + 7 = Amanda
Write an expression for Pam's age. Since 2 above is a function of Amanda, you'd use 1 above and substitute variables.
• p = u - 7
Pam is 16 years or older, show this as an inequality.
• p >= 16
• Pam is Greater than or Equal to 16.
Solve this to show an inequality for Amanda's age.
• u - 7 >= 16
• Substitute (u-7) for p as they are equal.
• (u - 7) + 7 >= 16 + 7
• u >= 23
• solving for u.
For anyone that couldn't follow what Brit was saying.

Regards,
SB

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7. Tahir2 Veteran

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Thanks for your help BRiT and Silent Buddha, my daughter is looking over your answers with a new insight. Hopefully she can figure out the rest for herself.

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8. Tahir2 Veteran

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My daughter looked at the answers and said that BRiT processed Jill's inequality rather than Tom's therefore not answering the question.

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9. BRiT (>• •)>⌐■-■ (⌐■-■) ModeratorLegendAlpha

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She is correct. As I disclaimered, lack of sleep.

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10. BRiT (>• •)>⌐■-■ (⌐■-■) ModeratorLegendAlpha

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Tim is half Jill's age, Jill is b years.
a) write an expression for Jill's age.
b) Tim is 14 years old or younger, show this as an inequality.
c) Show an inequality for Jill's age.

---
[ Turning the statements into math statements ]
Tim = 1/2 * Jill
Jill = b

Part a)
Therefore we need to rework it somewhat to get statement for Jill
Tim = 1/2 * b
[ multiply both sides by 2 ]
2 * Tim = b
[ restructure equation to be centered on Jill ]
B = 2 * Tim

a) b = 2 * Tim

Part b)
Turn the statment of Tim being 14 or youngerto an equation
Tim <= 14

Part c)
We have 2 statements that I think can be combined using substitution property
B = 2 * Tim
And
Tim <= 14

Produces
b = 2 * 14 [ at the greatest age of Tim who is 14 or younger ]

So if he's younger then Jills age becomes
b <= 2 * 14

Which reduces down to
b <= 28

.....

Seems like some parts end up the same, just maybe needed to flip the one equation to have Jill on the left side?

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11. Davros Legend

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what is an equality?

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12. tangey Veteran

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Yeah, I thought I was the only only that didn't recognise that term.

Also
Seems a very vague question. Solve WHAT ?

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13. zed Veteran

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Yeah what is inequality? Perhaps I understand it wrong been many years since I was in school maths
Looking on dictionary
which is what I thought it meant, yet Brit & Silent_Buddah are using <= , >= (≤ , ≥)
which to me is certainly not an inequality, but like I said been many years so perhaps they are right

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14. Tahir2 Veteran

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15. BRiT (>• •)>⌐■-■ (⌐■-■) ModeratorLegendAlpha

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Equality is: =
Any other mathematical sign is an inequality, includes: <, <=, >, >=, != or <>

At least howI parsed it.

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16. orangpelupa Elite Bug Hunter LegendVeteran

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>_<
\(^_^)/

...

Sorry.. I just can't help but think of those after reading your examples

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17. zed Veteran

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yes I agree
now I agree with <,>,!= (but not >=,<=)

x = 3, y = 3
x >= y (yes I agree this is true)
x is an inequality to y (but saying this just seems wrong to me )

you could be correct,( been a long time since I looked at this)

x >= x
x is an inequality to x, x is an equality to x (so both statements are correct?)

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18. smw Newcomer

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< and > are known as strict inequalities in contrast to ≥ and ≤ which are not strict, but all of them are inequalities.
While x ≥ x may seem strange, this is actually quite useful If you prove that x ≥ y and y ≥ x, this means that x = y. Also, if you are testing some assertion and you end up with something like x > y and y > x (i.e. strict), then your assertion is wrong (this can be used e.g. in counterexamples).

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19. zed Veteran

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Yes I agree with all that, my point is about calling them 'inequalities' eg
3 is an inequality of 3
To me that just sounds wrong, perhaps as a math term its correct, I don't know but I'll take yours words for it

A/ 3 is an equality of 3
B/ 3 is an inequality of 3
both A & B are correct

Are there any rational numbers that are not an inequality to any other rational number?
i.e. its a statement thats always true (though perhaps not for irrational numbers, though perhaps its also true for these as well?)

I'ld feel better about it by there being 3 terms
equality, quasequality (or something), inequality
I suppose you could argue 'strict inequality' but thats messy

#19
Last edited: Jan 17, 2018
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