Terrance has 3 times as many nickels as quarters. He has 8 fewer half dollars thank nickels. Altogether
Terrance has 3 times as many nickels as quarters. He has 8 fewer half dollars thank nickels. Altogether, Terrance has 153 coins. How many of each coin does Terrance have?
Plz answer this question
To solve this problem, let's assign variables to the unknown quantities:
Let's assume the number of quarters Terrance has is "q".
The number of nickels Terrance has is 3 times the number of quarters, so this can be written as 3q.
The number of half dollars Terrance has is 8 fewer than the number of nickels, so this can be written as 3q - 8.
To find the total number of coins Terrance has altogether, we add up the number of each type of coin:
Total number of coins = number of quarters + number of nickels + number of half dollars
Total number of coins = q + 3q + (3q - 8)
To simplify the expression, combine like terms:
Total number of coins = 7q - 8
Now, we need more information to solve the problem.
To solve this problem, we need to break it down into smaller steps.
Step 1: Define the variables
Let's define the variables:
Q = number of quarters
N = number of nickels
H = number of half dollars
Step 2: Translate the given information into equations
From the problem statement, we have the following information:
1. Terrance has 3 times as many nickels as quarters: N = 3Q
2. He has 8 fewer half dollars than nickels: H = N - 8
3. Altogether, we need to find the sum of the number of quarters, nickels, and half dollars: Q + N + H.
Step 3: Solve the equations
Replacing the variables N and H with their respective equations, we can rewrite the equation for the sum of the coins as follows:
Q + 3Q + (3Q - 8)
Combining like terms, we have:
7Q - 8
Therefore, the sum of the number of quarters, nickels, and half dollars is 7Q - 8.
Step 4: Find the solution
To find the value of Q, we need more information. The problem statement does not provide any additional information about the number of quarters. If we were given a specific value for Q, we could substitute it into the equation 7Q - 8 to find the total number of coins.
Without this additional information, we cannot determine the precise value of the sum of the coins. We can only describe it in terms of Q: 7Q - 8.
n = 3q
h = n-8
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