lavere has sixty-one coins, all of which are dimes and quaters. if the total value of the coins is $9.85, how many of each kind of coins has she?
Let the two numbers of coins be D and Q.
Solve this pair of equations:
D + Q = 61
10D + 25Q = 985 (total number of cents)
10D + 10 Q = 610
15 Q = 375
Q = ?
Take it from there
Q=25
To solve this problem, we can set up a system of equations. Let's represent the number of dimes as "d" and the number of quarters as "q".
We know that Lavere has a total of 61 coins, so we can write the equation:
d + q = 61 (Equation 1)
We also know that the total value of the coins is $9.85. Dimes are worth $0.10 each, so the total value of the dimes is 0.10d. Quarters are worth $0.25 each, so the total value of the quarters is 0.25q. We can write the equation for the total value as:
0.10d + 0.25q = 9.85 (Equation 2)
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method to solve for d and q.
First, multiply Equation 1 by 0.10 to eliminate the decimals:
0.10d + 0.10q = 6.10 (Equation 3)
Now, subtract Equation 3 from Equation 2 to eliminate the variable "d":
0.10d + 0.25q - (0.10d + 0.10q) = 9.85 - 6.10
0.10d - 0.10d + 0.25q - 0.10q = 3.75
0.15q = 3.75
Now, solve for q by dividing both sides of the equation by 0.15:
q = 3.75 / 0.15
q = 25
Now that we have the value of q, substitute it back into Equation 1 to find the value of d:
d + 25 = 61
d = 61 - 25
d = 36
Therefore, Lavere has 36 dimes and 25 quarters.