In vanessa's coin bank there are 4 times as many quaters as nickels, 2 fewer dimes than nickels, and 15 pennies. the total amount in the bank is $5.80. How many of each coin are in the bank? assign a variable to unknown and write an equation to find unknown.
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Let's assign variables to represent the unknowns in the problem:
Let Q = the number of quarters
Let N = the number of nickels
Let D = the number of dimes
From the problem, we know:
1. There are 4 times as many quarters as nickels: Q = 4N
2. There are 2 fewer dimes than nickels: D = N - 2
3. There are 15 pennies: P = 15
4. The total value in the bank is $5.80: 0.25Q + 0.05N + 0.10D + 0.01P = 5.80
The equation to find the unknown is:
0.25Q + 0.05N + 0.10D + 0.01P = 5.80
To solve this problem, let's assign variables to the unknown quantities. Let:
- x be the number of nickels,
- 4x be the number of quarters (since there are 4 times as many quarters as nickels),
- (x-2) be the number of dimes (since there are 2 fewer dimes than nickels).
We're given that there are 15 pennies, so we can ignore them for now.
Now, let's write an equation to find the unknown. The total value in the bank is $5.80, so we can set up the equation:
0.05x + 0.25(4x) + 0.10(x-2) + 0.01(15) = 5.80
In this equation, we're multiplying the number of each coin by its respective value (0.05 for nickels, 0.25 for quarters, 0.10 for dimes, and 0.01 for pennies), then adding them all up to equal the total value of $5.80.
Now, we can solve this equation to find the value of x.