Math / Algebra

QuestionA collection of nickels, dimes, and quarters consist of 13 coins with a total of $\$ 1.50$ . If the number o dimes is equal to the number of nickels, find the number of each type of coins.
There are $\square$ nickels, $\square$ dimes, and $\square$ quarters.

Studdy Solution

STEP 1

1. The collection consists of nickels, dimes, and quarters.
2. There are a total of 13 coins.
3. The total value of the coins is $1.50.
4. The number of dimes is equal to the number of nickels.
5. We need to find the number of each type of coin.

STEP 2

1. Define variables for the number of each type of coin.
2. Set up equations based on the given information.
3. Solve the system of equations to find the number of each type of coin.

STEP 3

Define variables for the number of each type of coin.
Let $n$ be the number of nickels, $d$ be the number of dimes, and $q$ be the number of quarters.

STEP 4

Set up equations based on the given information.
Since the number of dimes is equal to the number of nickels, we have: $d = n$
The total number of coins is 13: $n + d + q = 13$
The total value of the coins is $1.50, which is equivalent to 150 cents. The value equation is: \[ 5n + 10d + 25q = 150 \]

STEP 5

Substitute the equation $d = n$ into the other equations.
Substitute $d = n$ into the total number of coins equation: $n + n + q = 13$ $2n + q = 13$
Substitute $d = n$ into the value equation: $5n + 10n + 25q = 150$ $15n + 25q = 150$

STEP 6

Solve the system of equations.
From the equation $2n + q = 13$ , express $q$ in terms of $n$ : $q = 13 - 2n$
Substitute $q = 13 - 2n$ into the equation $15n + 25q = 150$ : $15n + 25(13 - 2n) = 150$ $15n + 325 - 50n = 150$ $-35n + 325 = 150$
Subtract 325 from both sides: $-35n = 150 - 325$ $-35n = -175$
Divide by -35: $n = \frac{-175}{-35}$ $n = 5$
Since $d = n$ , we have: $d = 5$
Substitute $n = 5$ into $q = 13 - 2n$ : $q = 13 - 2(5)$ $q = 13 - 10$ $q = 3$
The number of nickels is $\boxed{5}$ , the number of dimes is $\boxed{5}$ , and the number of quarters is $\boxed{3}$ .

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QuestionA collection of nickels, dimes, and quarters consist of 13 coins with a total of $\$ 1.50$ . If the number o dimes is equal to the number of nickels, find the number of each type of coins.
There are $\square$ nickels, $\square$ dimes, and $\square$ quarters.

Studdy Solution

STEP 1

1. The collection consists of nickels, dimes, and quarters.
2. There are a total of 13 coins.
3. The total value of the coins is $1.50.
4. The number of dimes is equal to the number of nickels.
5. We need to find the number of each type of coin.

STEP 2

1. Define variables for the number of each type of coin.
2. Set up equations based on the given information.
3. Solve the system of equations to find the number of each type of coin.

STEP 3

Define variables for the number of each type of coin.
Let $n$ be the number of nickels, $d$ be the number of dimes, and $q$ be the number of quarters.

STEP 4

Set up equations based on the given information.
Since the number of dimes is equal to the number of nickels, we have: $d = n$
The total number of coins is 13: $n + d + q = 13$
The total value of the coins is $1.50, which is equivalent to 150 cents. The value equation is: \[ 5n + 10d + 25q = 150 \]

STEP 5

Substitute the equation $d = n$ into the other equations.
Substitute $d = n$ into the total number of coins equation: $n + n + q = 13$ $2n + q = 13$
Substitute $d = n$ into the value equation: $5n + 10n + 25q = 150$ $15n + 25q = 150$

STEP 6

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QuestionA collection of nickels, dimes, and quarters consist of 13 coins with a total of $1.50\$ 1.50$1.50. If the number o dimes is equal to the number of nickels, find the number of each type of coins.There are □\square□ nickels, □\square□ dimes, and □\square□ quarters.

Studdy Solution

STEP 1

1. The collection consists of nickels, dimes, and quarters.2. There are a total of 13 coins.3. The total value of the coins is $1.50.4. The number of dimes is equal to the number of nickels.5. We need to find the number of each type of coin.

STEP 2

1. Define variables for the number of each type of coin.2. Set up equations based on the given information.3. Solve the system of equations to find the number of each type of coin.

STEP 3

Define variables for the number of each type of coin.Let n n n be the number of nickels, d d d be the number of dimes, and q q q be the number of quarters.

STEP 4

STEP 5

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionA collection of nickels, dimes, and quarters consist of 13 coins with a total of $\$ 1.50$ . If the number o dimes is equal to the number of nickels, find the number of each type of coins.
There are $\square$ nickels, $\square$ dimes, and $\square$ quarters.

1. The collection consists of nickels, dimes, and quarters.
2. There are a total of 13 coins.
3. The total value of the coins is $1.50.
4. The number of dimes is equal to the number of nickels.
5. We need to find the number of each type of coin.

1. Define variables for the number of each type of coin.
2. Set up equations based on the given information.
3. Solve the system of equations to find the number of each type of coin.

Define variables for the number of each type of coin.
Let $n$ be the number of nickels, $d$ be the number of dimes, and $q$ be the number of quarters.