A clerk was asked to change a $10 bill. She returned 9 more dimes than nickels and twenty-one more quarters than dimes. How many coins of each did she return?
Solve using the V.E.S.T. method.
A clerk was asked to change a $10 bill. She returned 9 more dimes than nickels and twenty-one more quarters than dimes. How many coins of each did she return?
X nickels.
(X+9) dimes.
(X+9)+21 = (X+30) qtrs.
5x + 10(x+9) + 25(x+30) = 1000 cents.
40x + 840 = 1000,
40x = 1000 - 840 = 160,
X = 4 Nickels.
X+9 = 13 Dimes.
X+30 = 34 Qtrs.
Sorry, but I don't know what V.E.S.T.
means.
To solve this problem using the V.E.S.T. method, we need to follow the steps:
1. Define variables: Let's assign variables to the unknown quantities.
Let N = the number of nickels
Let D = the number of dimes
Let Q = the number of quarters
2. Translate the problem into equations:
The total value of all the coins is equal to the value of the $10 bill, which is $10.
The value of the nickels is 5 cents each, so the total value of the nickels is 5N cents.
The value of the dimes is 10 cents each, so the total value of the dimes is 10D cents.
The value of the quarters is 25 cents each, so the total value of the quarters is 25Q cents.
We are given three conditions:
a) The clerk returns 9 more dimes than nickels: D = N + 9
b) The clerk returns twenty-one more quarters than dimes: Q = D + 21
c) The total value of all the coins is $10: 5N + 10D + 25Q = 1000 (since $10 is equal to 1000 cents)
3. Solve the equations:
Substitute conditions a) and b) in terms of N to condition c):
5N + 10(D = N + 9) + 25(D + 21) = 1000
5N + 10N + 90 + 25D + 525 = 1000
15N + 35D = 385
Rearrange condition c) to solve for N:
15N = 385 - 35D
N = (385 - 35D) / 15
Since N and D are whole numbers, we need to find values of D that make N a whole number.
4. Substitute values and solve for N, D, and Q:
Let's substitute the values of D and N into conditions a) and b) to find Q:
D = N + 9
Q = D + 21
Substituting (385 - 35D)/15 for N and (385 - 35D)/15 + 9 for D in Q:
Q = (385 - 35D)/15 + 21
We can plug in different values for D until we find a whole number solution for N, D, and Q. Let's start with D = 10:
N = (385 - 35*10)/15 = 23
Q = (385 - 35*10)/15 + 21 = 38
So, for D = 10, we have N = 23 and Q = 38.
Checking the conditions:
a) D = N + 9: 10 = 23 + 9 (true)
b) Q = D + 21: 38 = 10 + 21 (true)
c) 5N + 10D + 25Q = 1000: 5*23 + 10*10 + 25*38 = 1000 (true)
Therefore, the clerk returned 23 nickels, 10 dimes, and 38 quarters.
To solve this problem using the V.E.S.T. method, we will assign variables to represent the unknown quantities in the problem.
Let's use:
N = number of nickels
D = number of dimes
Q = number of quarters
According to the problem:
1. The clerk returned 9 more dimes than nickels, so D = N + 9.
2. The clerk also returned twenty-one more quarters than dimes, so Q = D + 21.
We're given that the clerk changed a $10 bill, so the total value of the coins returned should be $10. We can represent this equation as follows:
(0.05)N + (0.10)D + (0.25)Q = 10
Now, we can substitute the values of D and Q from equations 1 and 2 into the equation above:
(0.05)N + (0.10)(N + 9) + (0.25)(N + 9 + 21) = 10
Now we can solve this equation to find the value of N, which represents the number of nickels.