Notice that each such "minimal collection" of 9 grapes, 3 walnuts and 11 oranges (9g,3w,11o) contain 23 pieces of fruit.
Using your calculator if you prefer, notice that 161 is equal to 23*7 (23 times 7) by carrying out the division "161/23 = ?" and solving it...

Let's see how this starts, in thousands of dollars:
Yr | A | B
1 |20 | 25
2 |22.5 | 27
3| 25 | 29
etc
Notice every two years A goes up by 5 (in thousands) and B goes up by 4 so later we'll have:
5 | 30 | 33
7 | 35 | 37
9| 40...

Shelby,
Are you trying to compare the two fractions? If the following isn't what you need, could you please clarify what the requirement is and what exactly you're allowed and not allowed (other than not allowed common deminators). But notice this:
19/20 = 1 - 1/20 and
27/28...

[Edit of original] Sorry, I have seen several questions with typos in one night, so wondered whether the first = was supposed to be a multiplication in a number theory question I thought you perhaps intended.
To eliminate ambiguity, it would have helped to add 5 words, "where...

Hi, if x=3 is a root then (x-3) is a factor and since the multiplicity is 2, (x-3)^2 is a factor.
Next, since -3 is a root, then (x- (-3)) is a factor, that is, (x+3) is a factor, and in fact, (x+3)^3 is a factor since the multiplicity is 3.
Now, what about...

x+4(5/7)-8=6
now add 8 to both sides to get
x+4(5/7)=14
Re-write as x+ (20/7) = 14 but 14 = (98/7) so:
x+(20/7) = (98/7)
Hence: x = 98/7 - 20/7 = 78/7
Which is the same as x= 11 and 1/7. Let...

Hi, I think you mean "the square-root of pi"
Pi is the irrational number 3.14159265.... (pi is defined to be the number you get if you divide the circumference of a circle by its diameter, the preceding is an approximate decimal representation)
Now you can...

Let W be Rollie's initial weight, and let G stand for the "goal" weight.
Weight at beginning of first month: W
Weight lost during the first month: (1/3)(W - G) + 3
Weight at end of the first month: W - [(1/3)W - (1/3)G + 3] which you can simplify to:
(2/3)W +...

Hi, the area of any circle whose radius is "r" is given by the formula "pi * r * r" where the * means multiplication and where the Greek letter pi stands for the mathematical constant which is on your calculator and which is roughly 3.14159265....
We often write "r^2"...

Hi Ervin,
Since the question doesn't specify much more than "how to identify" I might not cover exactly what your daughter needs; if the following isn't enough feel free to follow up with a more detailed question. In short however:
A point is basically the geometric...