Select the equation that solves this problem:
Eleven coins (dimes and nickels) are worth 60 cents. How many dimes are
there?
a. 10d + 25(11 - d) = 170
b. 10d + 25(8 - d) = 170
c. 10d + 5(8 - d) = 60
d. 10d + 5(11 - d) = 60
Note that all the equations start with 10d, indicating that you are adding up the value of the coins.
So right away you know it's C or D
Since there are 11 coins, if there are d dimes, then there are 11-d nickels.
So, D
To solve this problem, we need to set up an equation that represents the information given. We know that the total value of the coins is 60 cents, and that there are eleven coins. Let's break down the problem:
Let d = the number of dimes
Since there are eleven coins in total, the number of nickels is (11 - d), since dimes and nickels together make up the total number of coins.
The value of dimes is 10 cents each, so the total value of all the dimes is 10d cents.
The value of nickels is 5 cents each, so the total value of all the nickels is 5(11 - d) cents.
Now we can set up the equation and solve for d:
10d + 5(11 - d) = 60
To determine which equation solves the problem, we can substitute the values from each option and see if the equation holds true:
a. 10d + 25(11 - d) = 170
b. 10d + 25(8 - d) = 170
c. 10d + 5(8 - d) = 60
d. 10d + 5(11 - d) = 60
By substituting the values of d into each equation, we can find which equation gives us the correct total value.