you have 40 coins, quarters dimes and nickles and they equal $6.00. you have two more quarters then nickles. how many of each do you have
let the number of nickels be x (nickels, not nickles)
then the number of quarters is x+2
then the number of dimes is 40 - x - (x+2)
or 38-2x
5x + 25(x+2) + 10(38-2x) = 600
solve
Let q = number of quarters
let d = number of dimes
let n = number of nickels.
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q + d + n = 40
0.25q + 0.10d + 0.05n = 6.00
q = n+2
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Solve for the three unknowns. Check my thinking.
Greg has 40 coins. Half of them are quarters and the rest are nickels. What is the value of the coins?
greg has 40 cents in his hand half of them are quarters and the rest are nickels
To solve this problem, let's break it down step by step.
Step 1: Assign variables
Let's assign variables to the unknowns in the problem:
- Let's call the number of quarters "Q"
- Let's call the number of dimes "D"
- Let's call the number of nickels "N"
Step 2: Set up equations
We have three pieces of information from the problem:
1) You have a total of 40 coins, so we can write the equation:
Q + D + N = 40
2) The value of all the coins is $6.00, so we can write the equation in terms of cents:
25Q + 10D + 5N = 600 (since a quarter is 25 cents, a dime is 10 cents, and a nickel is 5 cents)
3) You have two more quarters than nickels, so we can write another equation:
Q = N + 2
Step 3: Solve the equations
Now, we can solve the system of equations using substitution or elimination to find the values of Q, D, and N.
Let's use substitution method in this case:
From equation 3, we can substitute Q with (N + 2) in equation 1:
(N + 2) + D + N = 40
2N + D + 2 = 40
2N + D = 38 -- Equation 4
Now, substitute the value of Q in equation 2:
25(Q) + 10D + 5N = 600
25(N + 2) + 10D + 5N = 600
25N + 50 + 10D + 5N = 600
30N + 10D + 50 = 600
30N + 10D = 550 -- Equation 5
Now, we have two equations with two variables:
2N + D = 38 -- Equation 4
30N + 10D = 550 -- Equation 5
Step 4: Solve the equations
There are multiple ways to solve these equations, either by substitution, elimination, or graphing. In this case, let's solve it using the elimination method:
Multiply Equation 4 by 5 and Equation 5 by 1 to make the coefficients of N in both equations equal:
10N + 5D = 190 -- Equation 6
30N + 10D = 550 -- Equation 7
Subtract Equation 6 from Equation 7 to eliminate the N variable:
(30N + 10D) - (10N + 5D) = 550 - 190
20N + 5D = 360
4N + D = 72 -- Equation 8
Now, we have two equations with two variables:
4N + D = 72 -- Equation 8
2N + D = 38 -- Equation 4
Subtract Equation 4 from Equation 8 to eliminate the D variable:
(4N + D) - (2N + D) = 72 - 38
2N = 34
N = 17
Now, substitute the value of N into Equation 4 to find D:
2(17) + D = 38
34 + D = 38
D = 38 - 34
D = 4
Finally, substitute the values of N and D into Equation 3 to find Q:
Q = N + 2
Q = 17 + 2
Q = 19
Therefore, you have 19 quarters, 4 dimes, and 17 nickels.