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4 / 7 ==0.57142857142857142857142857142857........It has a repeating "period" of 6 digits.

Therefore: 2007 mod 6 ==3 - which means the last digit is the 3rd digit from the decimal point, which is a "1".

x = origianl amount

spending 3/8 ths leaves  5/8 x        spending 4/7 of this leaves   3/7  (5/8 x)   and this = 45

3/7 ( 5/8 x) = 45    solve for x

x = 168

They all bought the same number of fruits

Let 'x' be the number     d = price of orange    a = price of apple

5d + ( x-5)a = 7.80        <====== Multiply by -2.2 and add to the second equation ( this is to cancel ou the 'd')

11d + (x-11)a = 9.00

-2.2(x-5)a + (x-11)a = -2.2(7.80)(9.00)

simplifying this results in xa = 6.80         this is the amount Chris spent on 'x' apples

x = total numer of items

Luke has   3/8 x - 5      <==== this is given

   the remainder will be    x -  ( 3/8 x -5)     and this equals Miko's 25

x - (3/8 x - 5 ) = 25

5/8x + 5 = 25

x = 32 total items

The 4 square sides are all equal     32/4 = 8 inches = side length

   this is also the circle DIAMETER  so the circle radius = 4 inches

area of circle = pi r^2 =   pi 4^2 = 16 pi   in ²

a = b + 42      given     re written as    a-42 = b

then

(a-118) * 3 = (b+118)     sub in the red equation for b

3a - 354 = ( a-42    + 118 )

a = 215 originally ...... then he gives away 118   to have 97 in the end.

3/7 = 6/14 (fraction of total that are men)

1 - 3/7 = 4/7 = 8/14 
(fraction of total that are women and children)

⅝ × 4/7 = 5/14 
(fraction of the total that are women)

1 - 4/7 - 5/14 = 1 - 6/14 - 5/14 = 6/14
(fraction of the total that are children)


This tells you that ratio of men to women to children
= 6 : 5 : 3


Men → 2 vouchers each
Women → 8 vouchers each
Children → 5 vouchers each


Next, grouping concept.


6 men, 5 women, 3 children in 1 group.

Number of vouchers in 1 group 
= 6 × 2 + 5 × 8 + 3 × 5 
= 12 + 40 + 15
= 67

Number of groups 
= 1541 ÷ 67
= 23

Number of children = 23 groups × 3 per group
= 69

Number of vouchers collected by them
= 69 × 5
= 345

6 x 10 = 60 in²

5 x 9 = 45 

(60 -45)/60 x100% = 25% reduction

  men*2               women *8                     children * 5

3/7x * 2      +    5/8 (4/7)* 8 x       +      3/8 (4/7) x * 5   = 1541          x = number of people at event

(6/7 + 160/56 + 60/56 ) x = 1541

x = 322

children vouchers = 3/8 * 4/7  *5 * 322  = 345 vouchers

Not possible for AD   AND    EG    to BOTH equal 18.

10 people would half the time to 6 hours.....     20 people would half the 6 hours to 3 hours.

Like so:

As follows:

2*6*2*3

I traveled from Vertex Valley to Fraction Falls last week. I completed 3/5 of the distance in the morning and 2/3 of the remaining distance in the afternoon. I still had 12 miles to travel. What is the distance from Vertex Valley to Fraction Falls?      

Let X represent the total distance. 

X  =  3/5 of the distance + 2/3 of the remaining 2/5 of the distance + 12  

X  =  (3/5)X + (2/3)(2/5)X + 12 

X  =  3X/5 + 4X/15 + 12        It's necessary to convert all the denominators to the same number.    

X  =  (3/3)(3X/5) + 4X/15 + (15/15)(12)  

X  =  9X/15 + 4X/15 + 180/15  

X  =  (9X + 4X + 180) / 15      Next, to multiply both sides by 15   

15X  =  9X + 4X + 180            Next, to combine 9X + 4X to 13X and subtract it from both sides.  

2X  =  180  

  X  =  90                                The distance from Vertex Valley to Fraction Falls is 90 miles.   

Check answer:  

3/5 of 90 is 54.  That leaves 36 miles.  2/3 of 36 is 24.  That leaves 12 miles.  Answer checks out.  

_.

This is really EZ.  Just use induction.

Thanks again Alan,

Again, I did not do the initial integration properly.  

I must have been off with the pixies yesterday.

I'll try some more today.

Hopefully, the pixies will be covering from yesterday's party.

Thanks so much.  

You're welcome!   Hope you understood how to solve it.....    ~EP

A guest impersonating a guest.   Is that your humor input?  Yes, it is mildly amusing.

But still no 'thank you'.

Thank you!!! It was correct!

You can use the cosine law

d^2 = 4^2 + 6^2 - 2 (4)(6) cos 120                 (120 degrees is the angle between the two hiking segments)

d^2 = 76  

            d= sqrt 76 =8.72 miles from start

First clean up your equations by expanding and simplifying

4m-4n=7-7n

4m +3n = 7  

3/2 n = 4 - 2m

4m + 3n = 8

Both the same equation but they equal different constants.... there is NO SOLUTION....prallel lines do not cross/intersect.

Area of a rhombus =  (diagonal1 * diagonal2)/2  = 108 ft²

How many values of satisfy both of the following conditions?
(a) x is a multiple of 7, not necessarily positive.
(b) x^2 is less than 5000.

Hello Guest!

If \(x\in \mathbb Z\ then\)

\(x^2<5000\\ x<\sqrt{5000}\\ x<70.71\)

\(x\in \{-70,-63,-56,\ …\ 0,\ ...\ 56,\ 63,70\}\)

\(21\ values\ meet\ the\ two\ given\ conditions.\)

  !