A collection of thirty-seven coins consists of nickels, dimes and quarters. There are ten more dimes than nickels. Represent the value of all the coins using one variable.
number of nickels ---- x
number of dimes ----- x+10
number of quarters = 37-(x + x+10) = 27 - 2x
value of coins = 5x + 10(x+10) + 25(27-2x)
= 5x + 10x + 100 + 675 - 50x
= 775 - 35 x
To represent the value of all the coins using one variable, we can assign a variable to represent the number of nickels. Let's call it "n".
Since there are ten more dimes than nickels, the number of dimes can be represented as "n + 10".
The number of quarters can be represented as the remaining coins after subtracting the number of nickels and dimes from the total number of coins, which is 37. So, the number of quarters can be represented as "37 - n - (n + 10)".
Now, let's calculate the value of all the coins.
The value of one nickel is $0.05, so the value of all nickels can be represented as "0.05n".
The value of one dime is $0.10, so the value of all dimes can be represented as "0.10(n + 10)".
The value of one quarter is $0.25, so the value of all quarters can be represented as "0.25(37 - n - (n + 10))".
To represent the total value of all the coins using one variable, we can add up the values of nickels, dimes, and quarters:
Total value = value of nickels + value of dimes + value of quarters
Total value = 0.05n + 0.10(n + 10) + 0.25(37 - n - (n + 10))
Simplifying the expression will give us the final representation of the value of all the coins using one variable.