dave throws loose change in to a cup an takes it out every 2 weeks
this time it is all nickels and dimes
there are 7 times as many dimes as nickels and the value of dimes is $5.85 more than the value of the nickels
how many nickels and dimes does dave have
D = 7N
.10D - .05N = 5.85
Substitute 7N for D in the second equation and solve for N. Insert that value into the first equation to solve for D. Check by putting both values into the second equation.
To solve this problem, we need to set up a system of equations based on the given information.
Let's say the number of nickels is represented by "n" and the number of dimes is represented by "d".
From the problem statement, we know that there are 7 times as many dimes as nickels, so we can write the first equation as:
d = 7n
We also know that the value of the dimes is $5.85 more than the value of the nickels. Since the value of a nickel is $0.05 and the value of a dime is $0.10, we can write the second equation as:
0.10d = 0.05n + 5.85
Now we have a system of equations:
d = 7n
0.10d = 0.05n + 5.85
To solve the system, we can substitute the value of d from the first equation into the second equation:
0.10(7n) = 0.05n + 5.85
0.70n = 0.05n + 5.85
0.70n - 0.05n = 5.85
0.65n = 5.85
n = 5.85 / 0.65
n ≈ 9
Therefore, Dave has approximately 9 nickels.
To find the number of dimes, we can substitute the value of n into the first equation:
d = 7n
d = 7(9)
d = 63
Therefore, Dave has 63 dimes.
In conclusion, Dave has 9 nickels and 63 dimes.