Question

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

Answer 1

3 pennies, 9 nickels, and 6 dimes

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.