We have a jar of coins, all dimes and pennies. All together, we have 204 coins, and the total value of all coins in the jar is $ 10.41. How many dimes are there in the jar?

Answer 1

d represents the number of dimes

204 - d represents the number of pennies

0.10d + 0.01(204 - d) = 10.41

Can you solve for d and answer?

Answer 2

Mark's solution is great. To clarify some points:

When writing an equation from scratch, it helps to use letters for your variable that relate to what they represent. D = dimes in this equation.

With the information you have, you know d (dimes) + p (pennies) = 204 (total number of coins).

We don't know how many pennies we have, but you can always move your equation around to solve for another value. If d + p = 204, then we can subtract d on both sides to get p = 204 - d. Thus the number of pennies we have must be equal to the total (204) minus the number of dimes (d). Since we know p = 204 - d, you can now replace p with that quantity in the equation because they are equal to each other. So d + (204 - d) = 204 or d + (204 - d) = 10.41...

However, there is something wrong with the setup in the last equation I wrote. Last, we have to account for the dollar value, not just the number of coins. Since the problem is expressed in dollars and cents, we want to add numbers for the values of our coins. One dime is 0.10 dollars and one penny is 0.01 dollars. Plug this in to what we had and you get 0.10d + 0.01p = 10.41 or 0.10d + 0.01(204 - d) = 10.41. Now that all the variables in the equation are d (dimes), you can solve for the number of dimes we have in this jar.

0.10d + 2.04 - 0.01d = 10.41

0.09d + 2.04 = 10.41 combined like terms

0.09d = 8.37 moved the 2.04 over

d = 93 divided by 0.09

So we have 93 dimes in this jar. If you want to solve for the number of pennies, you can plug that back in for d ---> 93 + p = 204 and solve for p. p = 111.

You can also express this as a system of equations:

p + d = 204

0.10d + 0.01p = 10.41 and solve using substitution or elimination.

Answer 3

Try Mark's hint before reading this.

The second sentence translates into math as "all together D + P = 204, and D/10 + P/100 = 10.41". Subtract 10× the 2nd equation from the first to cancel the D terms and get

99.9 = 204 – 104.1 = D + P – (D + P/10) = 9P/10.

Therefore P = 999/9 = 111. Finally D = 204 – P = 204 – 111 = 93.