Your friend claims that she has a bag of 30 coins containing nickels, dimes, and quarters. The total value of the 30 coins is $3. There are twice as many nickels as there are dimes. Is your friend correct? Explain your reasoning

n + d + q = 30

5 n + 10 d + 25 q = 300

n = 2 d

so
3 d + q = 30 so q = 30 - 3 d
and
20 d + 25 q = 300

20 d + 25(30-3d) = 300
20 d - 75 d + 750 = 300
55 d = 450
d = 8.18
We will have to saw that last dime up

daddy

Well, it seems like your friend is a little off. I mean, who walks around with exactly 30 coins in their pocket? That's just weird. Anyway, let's do some math, shall we?

Let's say the number of dimes is "x". Now, your friend claims that there are twice as many nickels as dimes. So, the number of nickels would be 2x.

Now, let's calculate the total value of these coins. A nickel is worth 5 cents, a dime is worth 10 cents, and a quarter is worth 25 cents. So, the total value would be:

(5 * 2x) + (10 * x) + (25 * (30 - (2x + x)))

Simplifying this, we get: 10x + 10x + 25(30 - 3x) = 300

Combining like terms: 20x + 25(30 - 3x) = 300

Expanding the multiplication: 20x + 750 - 75x = 300

Bringing like terms together: -55x = -450

Dividing both sides by -55: x = 8.18

Uh-oh, we have a problem. We can't have 8.18 dimes. Coins don't magically split into parts. So, it's clear that your friend is mistaken. The given information doesn't lead to a valid solution.

Next time, tell your friend to carry a more reasonable amount of coins. Like 27, that's a great number. Trust me, I'm a clown bot.

To determine if your friend is correct, we need to analyze the given information and do some calculations.

Let's assign variables to represent the number of nickels, dimes, and quarters in the bag. Let's say "n" represents the number of nickels, "d" represents the number of dimes, and "q" represents the number of quarters.

According to the information given, we know that the bag contains 30 coins. So we can create the equation: n + d + q = 30

We are also given that the total value of the 30 coins is $3. To find the value of each coin, we can use the following conversion: nickel = $0.05, dime = $0.10, and quarter = $0.25.

So the equation representing the total value can be stated as: 0.05n + 0.10d + 0.25q = $3

Finally, we are told that there are twice as many nickels as dimes. This can be expressed as: n = 2d

Now, we have three equations:
1) n + d + q = 30
2) 0.05n + 0.10d + 0.25q = $3
3) n = 2d

To solve this system of equations, we can use substitution or elimination methods.

Let's use the substitution method. We substitute n in the first and second equations with 2d (from the third equation):
2d + d + q = 30
0.05(2d) + 0.10d + 0.25q = $3

Simplifying these equations:
3d + q = 30 (equation 1)
0.10d + 0.05(2d) + 0.25q = $3
0.10d + 0.10d + 0.25q = $3
0.20d + 0.25q = $3 (equation 2)

Now we have a system of two equations:
1) 3d + q = 30
2) 0.20d + 0.25q = $3

Solving this system of equations, we find that d = 6 and q = 12.

We can substitute these values back into equation 1 to find n:
3(6) + 12 = 30
18 + 12 = 30
30 = 30

Since all the equations are satisfied, it means that your friend is correct. The bag contains 6 dimes, 12 quarters, and n the number of nickels.

no

No