There are 41 coins; the total is $3.45. Nickels and dimes .how many dimes are there ?

Answer 1

If we let n represent the number of nickels we have and d represent the number of dimes, we can come up with two equations.

n + d = 41 (the total number of coins we have is 41)

0.05n + 0.10d = 3.45 (0.05 and 0.10 come from the monetary worth of nickels and dimes)

From there, we can solve one equation for a variable and then plug it in to the second equation. For simplicity, let's solve the first equation for n. Subtracting d from both sides, we end up with n = 41 - d. Let's put that into the second equation.

0.05(41 - d) + 0.10d = 3.45

2.05 - 0.05d + 0.10d = 3.45 (distributive property)

2.05 + 0.05d = 3.45 (combine like terms)

0.05d = 1.40 (subtract 2.05 from both sides)

d = 28 (divide both sides by 0.05)

Therefore, we have 28 dimes. We can then use this knowledge to solve the first equation for n.

n + 28 = 41

n = 13

So, we have 28 dimes and 13 nickels.

If you want to check your work, we can see that 0.05(13) + 0.10(28) does in fact equal 3.45.

Answer 2

Set up the system of linear equations. Let n = # of nickels and d = # of dimes.

0.05n + 0.10d = 3.45

n + d = 41

Multiply the top equation by 20 and the bottom equation by -1.

n + 2d = 69

-n - d = -41

Eliminate the n so we can solve for d. Therefore, d = 28. There are 28 dimes.