Question

Your pocket contains a mixture of nickels and dimes which totals 75 cents. Set up a linear equation and find the number of nickels and dimes if there are 12 coins total.

A) 5n + 10d = 75; n + d = 12
B) 10n + 5d = 75; n - d = 12
C) 5n + 5d = 75; n + d = 12
D) 10n + 10d = 75; n + d = 12

Answer 1

To find the number of nickels and dimes in a mixture totaling 75 cents, set up a system of equations and solve for the variables n and d. The correct equation is A) 5n + 10d = 75; n + d = 12. The solution is n = 9, d = 3, so there are 9 nickels and 3 dimes in the pocket.

Step-by-step explanation:

To solve this problem, we can set up a system of equations:

n + d = 12 (equation 1)

0.05n + 0.10d = 0.75 (equation 2)

In equation 1, n represents the number of nickels and d represents the number of dimes. In equation 2, 0.05n represents the value of the nickels and 0.10d represents the value of the dimes, which should total 0.75 dollars or 75 cents.

To solve the system of equations, we can multiply equation 1 by 0.05 and subtract it from equation 2:

0.05n + 0.10d = 0.75

-0.05n - 0.05d = -0.60

Simplifying:

0.05d = 0.15

d = 3

Substituting the value of d into equation 1:

n + 3 = 12

n = 9

Therefore, there are 9 nickels and 3 dimes.