Nadia has 32 coins made up of nickles, dimes, and quarters. The sum of the number of nickels and the number of quarters is three times the number of dimes. If the total value of the coins is $4.60, how many of each kind does she have?
I can't figure out how to make this word problem into 3 equations.
Well, it seems like Nadia has quite the coin collection! Let's break down the information given and try to solve it with a touch of humor.
Let's say Nadia has x nickels, y dimes, and z quarters in her collection. We can start building our equations based on the given information.
First, we know that the sum of the number of nickels and the number of quarters is three times the number of dimes. So, our first equation is:
x + z = 3y (Equation 1)
(Three times as many dimes, sounds like a pretty dim-ensional equation, don't you think? 😄)
Now, let's look at the total value of the coins. Since we're dealing with different denominations, we need to multiply the number of each coin by its respective value. Nickels are worth $0.05, dimes are $0.10, and quarters are $0.25.
The total value of the nickels is 0.05x, the total value of the dimes is 0.10y, and the total value of the quarters is 0.25z. Adding these up should give us the total value of $4.60.
0.05x + 0.10y + 0.25z = 4.60 (Equation 2)
(Seems like a coin-tastic algebraic equation, doesn't it? 😁)
We're almost there! Now let's bring in the number of coins. We know Nadia has a total of 32 coins, so we can form our third equation:
x + y + z = 32 (Equation 3)
(32 coins? That's quite a wealth of coins! 💰)
And there you have it! We now have our three equations:
x + z = 3y (Equation 1)
0.05x + 0.10y + 0.25z = 4.60 (Equation 2)
x + y + z = 32 (Equation 3)
Now you can solve these equations and find out how many nickels, dimes, and quarters Nadia has. Good luck, and remember, math problems are always better with a sprinkle of humor!
To solve this word problem, we can break it down into three equations using the given information.
Let's use the following variables:
N = number of nickels
D = number of dimes
Q = number of quarters
Equation 1: "The sum of the number of nickels and the number of quarters is three times the number of dimes."
This can be written as: N + Q = 3D
Equation 2: "Nadia has 32 coins made up of nickels, dimes, and quarters."
This implies that the total number of coins is 32: N + D + Q = 32
Equation 3: "The total value of the coins is $4.60."
We need to consider the value of each coin. The value of a nickel is $0.05, a dime is $0.10, and a quarter is $0.25. Therefore, the equation for the total value is: 0.05N + 0.10D + 0.25Q = 4.60
Now we have a system of three equations. By solving this system, we can find the values of N, D, and Q.