Jessica's bank contains 18 quarters and dimes, of which q are quarters. Find the total value of the coins in dollars.
.25q + .10(18-q)
Thanks, Steve.
To find the total value of the coins in dollars, we need to determine the value of each quarter and each dime, and then calculate the sum.
Let's assign a variable to the number of quarters: q
Since Jessica has a total of 18 quarters and dimes, we can calculate the number of dimes using the equation:
18 - q = d (where d represents the number of dimes)
Now, let's determine the value of each quarter and each dime:
The value of a quarter is $0.25 (25 cents).
The value of a dime is $0.10 (10 cents).
To calculate the total value in dollars, we need to multiply the number of quarters by $0.25 and the number of dimes by $0.10, and then sum the results:
Value of quarters = q * $0.25
Value of dimes = d * $0.10
Total value = (q * $0.25) + (d * $0.10)
Substituting the expression for d in terms of q:
Total value = (q * $0.25) + ((18 - q) * $0.10)
Now we can simplify the equation:
Total value = $0.25q + $0.10(18 - q)
Expanding the equation:
Total value = $0.25q + $1.80 - $0.10q
Combining like terms:
Total value = $0.25q - $0.10q + $1.80
Simplifying further:
Total value = $0.15q + $1.80
Therefore, the total value of the coins in dollars is $0.15q + $1.80.