How do I figure out this problem? You have 37 coins (all nickels , dimes, and quarters) adding up to $5.50. You have 4 more quarters than nickels. How many dimes do you have?
Let q,d and n stand for the number of quarters, dimes and nickels you have respectively. Thus we know
(1) q + d + n = 37
(2) .25q + .10d + .05n = 5.50
(3) q = n + 4
We can use (3) to eliminate q in (1) and (2) to get
(n+4) + d + n= 37 or
(1') 2n +d =33
.25(n+4) + .10d + .05n = 5.50 or,
.25n + 1 +.1d +.05n = 5.50 so
(2').30n +.10d =4.50
From (1') d = 33-2n Use that for d in (2') to solve for n. Let us know if you need further help.
Thanks
To solve this problem, we need to set up a system of equations based on the given information.
Let's assign variables to the number of quarters (q), dimes (d), and nickels (n) you have.
From the problem statement, we can conclude three things:
1. The total number of coins is 37, so we have the equation:
q + d + n = 37
2. The total value of the coins is $5.50. Since a quarter is worth $0.25, a dime is worth $0.10, and a nickel is worth $0.05, we can write the equation:
0.25q + 0.10d + 0.05n = 5.50
3. You have 4 more quarters than nickels, so we can write the equation:
q = n + 4
Now, we have a system of three equations:
q + d + n = 37
0.25q + 0.10d + 0.05n = 5.50
q = n + 4
To solve the system of equations, we will use the method of substitution or elimination.
Let's use substitution in this case. From equation 3, we have q = n + 4. We can substitute this into the other equations to eliminate q.
Substituting q = n + 4 in equation 1, we get:
(n + 4) + d + n = 37
Simplifying, we have:
2n + d = 33
Similarly, substituting q = n + 4 in equation 2, we get:
0.25(n + 4) + 0.10d + 0.05n = 5.50
Simplifying, we have:
0.30n + 0.10d = 4.50
Now, we have a new system of equations:
2n + d = 33
0.30n + 0.10d = 4.50
To solve this system, we can use various methods like substitution, elimination, or graphing.
One approach is to solve equation 1 for d in terms of n:
d = 33 - 2n
Now, substitute this expression for d in equation 2:
0.30n + 0.10(33 - 2n) = 4.50
Simplifying, we have:
0.30n + 3.30 - 0.20n = 4.50
Combine like terms:
0.10n = 1.20
Divide both sides by 0.10:
n = 12
Now that we have found the value of n (nickels), we can substitute it back into equation 3 to find q (quarters):
q = n + 4 = 12 + 4 = 16
Finally, we can substitute the values of n and q into equation 1 to find d (dimes):
16 + d + 12 = 37
d + 28 = 37
d = 9
Therefore, you have 9 dimes.