A box contains 83 coins, only dimes and nickels. The amount of money in the box is $5.80. How many dimes and how many nickels are in the box?

Step-by-step explanation:

n = nickels

d = dimes

q = quarters

1)  n + d + q = 39

n+d = q - 3

Translate to:  2)   n + d - q = -3

.05n + .1d + .25q = 6.7   amount of each coin times the number of coins must add to 6.7

Multiply both sides by 20...

3)  1n + 2d + 5q = 134

Combine 1) & 2)

n + d + q = 39

n + d  - q = -3

Add together

2n + 2d = 36

Divide by 2:

4)  n + d = 18

Combine 1) and 3)

n + d + q = 39         Multiply by -5 =>  -5n -5d -5q = -195

n + 2d + 5q = 134                              n + 2d + 5q = 134

Add together->                                 5)   -4n - 3d  = -61

Combine 4) and 5)

  n + d = 18   Multiply by 4 =>  4n + 4d = 72

-4n - 3d = 61                          -4n - 3d = -61

Add:                                               d = 11

11 dimes...

Plug that into 4)

n + 11 = 18

n = 18-11 = 7 nickels.

Plug that into 1.

n + d + q = 39

7 + 11 + q = 39

18 + q = 39

q = 39-18 = 21 quarters

21 quarters, 7 nickels, and 11 dimes.

21(.25) + 7(.05) + 11(.1) = 5.25 + .35 + 1.1 = 5.6 + 1.1 = 6.7   Check.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

so, converting firstly the mixed fractions to improper fractions and then "adding".