A collection of nickels, dimes and pennies has an average value of 7¢ per coin. If a nickel were replaced by five pennies, the

average would drop to 6¢ per coin. What is the number of dimes in the collection?

Guest Nov 4, 2019

#1**+4 **

Solve the following system:

{3 + 10 d + 5 n = 168 | (equation 1)

5 + 10 d + 5 (n - 1) + p = 168 | (equation 2)

d + n + p = 24 | (equation 3)

Express the system in standard form:

{5 n + 10 d+0 p = 165 | (equation 1)

5 n + 10 d + p = 168 | (equation 2)

n + d + p = 24 | (equation 3)

Subtract equation 1 from equation 2:

{5 n + 10 d+0 p = 165 | (equation 1)

0 n+0 d+p = 3 | (equation 2)

n + d + p = 24 | (equation 3)

Divide equation 1 by 5:

{n + 2 d+0 p = 33 | (equation 1)

0 n+0 d+p = 3 | (equation 2)

n + d + p = 24 | (equation 3)

Subtract equation 1 from equation 3:

{n + 2 d+0 p = 33 | (equation 1)

0 n+0 d+p = 3 | (equation 2)

0 n - d + p = -9 | (equation 3)

Swap equation 2 with equation 3:

{n + 2 d+0 p = 33 | (equation 1)

0 n - d + p = -9 | (equation 2)

0 n+0 d+p = 3 | (equation 3)

Subtract equation 3 from equation 2:

{n + 2 d+0 p = 33 | (equation 1)

0 n - d+0 p = -12 | (equation 2)

0 n+0 d+p = 3 | (equation 3)

Multiply equation 2 by -1:

{n + 2 d+0 p = 33 | (equation 1)

0 n+d+0 p = 12 | (equation 2)

0 n+0 d+p = 3 | (equation 3)

Subtract 2 × (equation 2) from equation 1:

{n+0 d+0 p = 9 | (equation 1)

0 n+d+0 p = 12 | (equation 2)

0 n+0 d+p = 3 | (equation 3)

n = 9 Nickels

d = 12 Dimes

p = 3 Pennies

SVS2652 Nov 4, 2019