Math / Algebra

QuestionSelect the correct answer.
Kevin has $\$ 4.85$ in nickels and dimes. If he has 34 fewer dimes than nickels, how many coins (nickels and dimes) does he have altogether? A. 74 coins B. 75 coins C. 76 coins D. 77 coins

Studdy Solution

STEP 1

What is this asking? How many nickels and dimes does Kevin have if he has $\$4.85$ total, and $34$ fewer dimes than nickels? Watch out! Don't mix up the values of nickels ( $5$ cents) and dimes ( $10$ cents)!

STEP 2

1. Set up variables and equation
2. Solve for the number of nickels
3. Solve for the number of dimes
4. Calculate the total number of coins

STEP 3

Let $n$ be the number of nickels and $d$ be the number of dimes.
We know a nickel is worth $\$0.05$ , and a dime is worth $\$0.10$ .

STEP 4

We're told Kevin has $\$4.85$ in total.
We can write this as an equation: $0.05n + 0.10d = 4.85$ This equation represents the total value of his coins.

STEP 5

We also know he has $34$ fewer dimes than nickels.
Mathematically, this means: $d = n - 34$ This equation relates the number of nickels and dimes.

STEP 6

Now, let's substitute the second equation into the first equation.
This way, we get an equation with only one variable, $n$ : $0.05n + 0.10(n - 34) = 4.85$

STEP 7

Distribute the $0.10$ : $0.05n + 0.10n - 3.40 = 4.85$

STEP 8

Combine the $n$ terms: $0.15n - 3.40 = 4.85$

STEP 9

Add $3.40$ to both sides of the equation: $0.15n = 4.85 + 3.40$ $0.15n = 8.25$

STEP 10

Divide both sides by $0.15$ to find $n$ : $n = \frac{8.25}{0.15}$ $n = 55$ So, Kevin has $55$ nickels!

STEP 11

We know $d = n - 34$ , and we just found that $n = 55$ .
Let's substitute $n = 55$ into this equation: $d = 55 - 34$ $d = 21$ Kevin has $21$ dimes!

STEP 12

To find the total number of coins, we simply add the number of nickels and dimes: $55 + 21 = 76$

STEP 13

Kevin has a total of $\textbf{76}$ coins.
So the correct answer is C.

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QuestionSelect the correct answer.
Kevin has $\$ 4.85$ in nickels and dimes. If he has 34 fewer dimes than nickels, how many coins (nickels and dimes) does he have altogether? A. 74 coins B. 75 coins C. 76 coins D. 77 coins

Studdy Solution

STEP 1

What is this asking? How many nickels and dimes does Kevin have if he has $\$4.85$ total, and $34$ fewer dimes than nickels? Watch out! Don't mix up the values of nickels ( $5$ cents) and dimes ( $10$ cents)!

STEP 2

1. Set up variables and equation
2. Solve for the number of nickels
3. Solve for the number of dimes
4. Calculate the total number of coins

STEP 3

Let $n$ be the number of nickels and $d$ be the number of dimes.
We know a nickel is worth $\$0.05$ , and a dime is worth $\$0.10$ .

STEP 4

We're told Kevin has $\$4.85$ in total.
We can write this as an equation: $0.05n + 0.10d = 4.85$ This equation represents the total value of his coins.

STEP 5

We also know he has $34$ fewer dimes than nickels.
Mathematically, this means: $d = n - 34$ This equation relates the number of nickels and dimes.

STEP 6

Now, let's substitute the second equation into the first equation.
This way, we get an equation with only one variable, $n$ : $0.05n + 0.10(n - 34) = 4.85$

STEP 7

Distribute the $0.10$ : $0.05n + 0.10n - 3.40 = 4.85$

STEP 8

Combine the $n$ terms: $0.15n - 3.40 = 4.85$

STEP 9

Add $3.40$ to both sides of the equation: $0.15n = 4.85 + 3.40$ $0.15n = 8.25$

STEP 10

Divide both sides by $0.15$ to find $n$ : $n = \frac{8.25}{0.15}$ $n = 55$ So, Kevin has $55$ nickels!

STEP 11

We know $d = n - 34$ , and we just found that $n = 55$ .
Let's substitute $n = 55$ into this equation: $d = 55 - 34$ $d = 21$ Kevin has $21$ dimes!

STEP 12

To find the total number of coins, we simply add the number of nickels and dimes: $55 + 21 = 76$

STEP 13

Kevin has a total of $\textbf{76}$ coins.
So the correct answer is C.

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QuestionSelect the correct answer.Kevin has $4.85\$ 4.85$4.85 in nickels and dimes. If he has 34 fewer dimes than nickels, how many coins (nickels and dimes) does he have altogether? A. 74 coins B. 75 coins C. 76 coins D. 77 coins

Studdy Solution

STEP 1

What is this asking? How many nickels and dimes does Kevin have if he has $4.85\$4.85$4.85 total, and 343434 fewer dimes than nickels? Watch out! Don't mix up the values of nickels (555 cents) and dimes (101010 cents)!

STEP 2

1. Set up variables and equation2. Solve for the number of nickels3. Solve for the number of dimes4. Calculate the total number of coins

STEP 3

Let nnn be the number of **nickels** and ddd be the number of **dimes**.We know a nickel is worth $0.05\$0.05$0.05, and a dime is worth $0.10\$0.10$0.10.

STEP 4

We're told Kevin has $4.85\$4.85$4.85 in total.We can write this as an equation: 0.05n+0.10d=4.850.05n + 0.10d = 4.850.05n+0.10d=4.85 This equation represents the **total value** of his coins.

STEP 5

We also know he has 343434 fewer dimes than nickels.Mathematically, this means: d=n−34d = n - 34d=n−34 This equation relates the **number** of nickels and dimes.

STEP 6

Now, let's **substitute** the second equation into the first equation.This way, we get an equation with only one variable, nnn: 0.05n+0.10(n−34)=4.850.05n + 0.10(n - 34) = 4.850.05n+0.10(n−34)=4.85

STEP 7

**Distribute** the 0.100.100.10: 0.05n+0.10n−3.40=4.850.05n + 0.10n - 3.40 = 4.850.05n+0.10n−3.40=4.85

STEP 8

**Combine** the nnn terms: 0.15n−3.40=4.850.15n - 3.40 = 4.850.15n−3.40=4.85

STEP 9

**Add** 3.403.403.40 to both sides of the equation: 0.15n=4.85+3.400.15n = 4.85 + 3.400.15n=4.85+3.40 0.15n=8.250.15n = 8.250.15n=8.25

STEP 10

**Divide** both sides by 0.150.150.15 to find nnn: n=8.250.15n = \frac{8.25}{0.15}n=0.158.25​ n=55n = 55n=55So, Kevin has **555555 nickels**!

STEP 11

We know d=n−34d = n - 34d=n−34, and we just found that n=55n = 55n=55.Let's **substitute** n=55n = 55n=55 into this equation: d=55−34d = 55 - 34d=55−34 d=21d = 21d=21Kevin has **212121 dimes**!

STEP 12

To find the total number of coins, we simply **add** the number of nickels and dimes: 55+21=7655 + 21 = 7655+21=76

STEP 13

Kevin has a total of 76\textbf{76}76 coins.So the correct answer is C.

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Start learning now

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

QuestionSelect the correct answer.
Kevin has $\$ 4.85$ in nickels and dimes. If he has 34 fewer dimes than nickels, how many coins (nickels and dimes) does he have altogether? A. 74 coins B. 75 coins C. 76 coins D. 77 coins

What is this asking? How many nickels and dimes does Kevin have if he has $\$4.85$ total, and $34$ fewer dimes than nickels? Watch out! Don't mix up the values of nickels ( $5$ cents) and dimes ( $10$ cents)!

1. Set up variables and equation
2. Solve for the number of nickels
3. Solve for the number of dimes
4. Calculate the total number of coins

Let $n$ be the number of nickels and $d$ be the number of dimes.
We know a nickel is worth $\$0.05$ , and a dime is worth $\$0.10$ .

We're told Kevin has $\$4.85$ in total.
We can write this as an equation: $0.05n + 0.10d = 4.85$ This equation represents the total value of his coins.

We also know he has $34$ fewer dimes than nickels.
Mathematically, this means: $d = n - 34$ This equation relates the number of nickels and dimes.

Now, let's substitute the second equation into the first equation.
This way, we get an equation with only one variable, $n$ : $0.05n + 0.10(n - 34) = 4.85$

Distribute the $0.10$ : $0.05n + 0.10n - 3.40 = 4.85$

Combine the $n$ terms: $0.15n - 3.40 = 4.85$

Add $3.40$ to both sides of the equation: $0.15n = 4.85 + 3.40$ $0.15n = 8.25$

Divide both sides by $0.15$ to find $n$ : $n = \frac{8.25}{0.15}$ $n = 55$ So, Kevin has $55$ nickels!

We know $d = n - 34$ , and we just found that $n = 55$ .
Let's substitute $n = 55$ into this equation: $d = 55 - 34$ $d = 21$ Kevin has $21$ dimes!

To find the total number of coins, we simply add the number of nickels and dimes: $55 + 21 = 76$

Kevin has a total of $\textbf{76}$ coins.
So the correct answer is C.