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sasha has some pennies nickels and dimes in her pocket. the number of coins is 18 the expression is 0.01p+0.05n+0.10d represents the value of the coins which is 1.08 she has twice as many dimes as pennies. How many of each coin does Sasha have

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Answer:

3 pennies, 9 nickels, and 6 dimes

Step-by-step explanation:

We have three conditions:

(1)         p +        n +        d = 18

(2) 0.01p + 0.05n + 0.10d = 1.08

(3)                                   d = 2p

Multiply (2) by 100 and rearrange (3) to get a standard array.

(4)      p +   n +     d =   18

(5)      p + 5n + 10d = 108

(6)  -2p          +     d =    0

Subtract (4) from (5). This gives

(4)      p +   n +   d =  18

(7)            4n + 9d = 90

(6)  -2p          +   d =   0

Multiply (4) by 2 and add to (6). This gives

(4) p +   n +    d =  18

(7)        4n + 9d = 90

(8)        2n + 3d = 36

Double (8) and subtract from (7). This gives

(4)      p +   n +   d = 18

(7)            4n + 9d = 90

(9)                    3d = 18

Divide (9) by 3. This gives

(10) d = 6

Substitute (10) into (7). This gives

4n + 9(6) = 90

4n +   54 = 90

4n           = 36

(11) n       =    9

Substitute (10) and (11) into (4). This gives

p + 9 + 6 = 18

p +      15 = 18

p              =  3

Sasha has 3 pennies, 9 nickels, and 6 dimes.

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