jhazerybrown2

From above figure given measurements are,

12 mi, 5 mi, 9 mi, 5 mi, 3 mi, 3 mi, 6 mi, 3 mi and 5 mi

5 - 3 = 2 mi

9 + 3 = 12 mi

5 - 2 = 3 mi

5 + 3 = 8 mi

12 mi - (3 + 6) mi

12 - 9 = 3 mi

here we using formulas:

Area of right triangle = 1/2 * base * height and, Area of rectangle = length * width

Here Total area of the figure 

= Area of triangle + Area of rectangle + Area of rectangle + Area of rectangle + Area of triangle

= 1/2 * 12 * 8 + 9 * 3 + 9 * 2 + 12 * 3 + 1/2 * 3 * 3

= 48 + 27 + 18 + 36 + 9/2 

= 129 + 4.5

= 133.5

Total area of the figure = 133.5 mi2

I think I seen this problem 

Let total money of Tobias is $x

He spent amount of money in backpack is

$3x/7

Remaining amount = $(x - 3x/7) = $4x/7

Total money spent on 3 purification bottles is $(4x/7 * 2/3) = $8x/21

Remaining amount = $(4x/7 - 8x/21)

                               = $((12x - 8x))/21)

                               = $4x/21

Cost of 3 first aid kits = $4x/21 

Cost of each first aid kits = $(4x/21 / 3)

                                        = $4x/63

Cost of each purification bottles = $(8x/21 / 3)

                                                   = $8x/63

According to our problem

                8x/63 - 4x/63 = 14.80

                 => 4x/63 = 14.80

                 => 4x = (14.80) (63)

                 => x = ((14.80) (63))/4

                 => x = 233.10

The amount of money spent on backpack

          = $ (3/7 * 233.10)

          = $ 99.90

Remaining amount = $(233.10 - 99.90)

                               = $133.20

The amount of money spent on purification bottles = $(2/3 * 133.20)

           = $88.80

Thus the total amount of money spent on backpack and purification bottles is $(99.90 + 88.80) = $188.70

The total amount of money spent on backpack and purification bottles is $188.70
      
 

5. 

1/3 part of salary = $390

Total salary = $390*3/1 = $1170

Amount given to parents = $1170*4/9 = $520

Remaining money = Total salary - Spending on food - Amount given to parents

= $1170 - $390 - $520 = $260

Amount saved = 1/2 of remaining money

= $260*1/2 = $130
 

Money saved = $130

6. 

Let, the cost of each chocolate bar = x

Cost of each pack of potato chips = y

so,

=> 5x + 6y = 2/9 * 243

=> 5x +6y =54............(i)

and,

=> 3y = 2x

=> y = 2/3x................(ii)

Substituting value of y in (i):
=> 5x + 6(2/3x) = 54

=> 5x + 4x = 54

=> 9x = 54

=> x = 54/9

=> x = 6

Substituting value of x in (ii):

=> y = 2/3(6)

=> y = 4

So,

Cost of each chocolate bar = $6

Cost of each pack of potato chips = $4
 

Amount of money left = (1 - 2/9) * 243 = 7/9 * 243 = $189

Finding greatest number of chocolate bars he cay buy:
=> 189/6

=> 31.5

so,

Greatest number of chocolate bars he cay buy = 31

I will solve the first question 

a.

Daily spending by Peter = $1.20 

Daily spending by Cindy = 1 2/3 of Peter's daily spending = $1.20 * 1 2/3 = $1.20 * 5/3 = $2.00

Cindy started spending 15 days after Peter started. When Cindy spent all of her money, she had spent $11.60 more than Peter.

Let 'n' be the number of days takes Cindy to spend all the money. Therefore

Cindy's total spending -- $11.60 = Peter's total spending

($2.00 * n) + $11.60 = $1.20 * (n + 15)

2n - 11.60 = 1.20n + 18 

0.80n = 29.60

n = 29.60/0.80

n = 37

b.

Number of days taken by Peter = Number of days taken by Cindy to spend all money + 15 = 37 + 15 = 52 days

The total spending of Peter when Cindy had spent all the money is 

Total spending = Number of days * Daily spending = $52 * $1.20 = $62.40

a. Cindy took 37 days to spend all of her money. 

b. Peter had spent $62.40 in total when Cindy spent all of her money. 
 

It's not that hard :)

Brandon's steps were twice as long as Lucie's. Therefore, when Lucie moved ten steps forward, Brandon moved twenty steps forward. Because the map said to move ten steps forward and then turn left and move another ten steps forward, Brandon was already at the spot where the treasure was located.

In order for the system to have infinitely many solutions, k and m must both be equal to zero.

To get k = 2 and m = 0, you would need to modify the system to be:

3a + 2b = 2

6a + 2b = 2 + 3a + 0b

This system will have infinitely many solutions (a,b), with k = 2 and m = 0.