Math / Algebra

QuestionThe ratio of guitar players to drummers who tried out for a band is $35: 21$ . If there are 140 guitar players, how many drummers are there? label required

Studdy Solution

STEP 1

What is this asking? If we know the proportion of guitar players to drummers, and the total number of guitar players, how many drummers tried out? Watch out! Don't mix up the guitar players and drummers!
Keep track of which number goes with which instrument.

STEP 2

1. Simplify the Ratio
2. Set up a Proportion
3. Solve for the Number of Drummers

STEP 3

Alright, let's simplify that ratio of guitar players to drummers!
We've got $35:21$ .
Both of these numbers are divisible by 7.

STEP 4

Dividing both sides of the ratio by 7, we get $\frac{35}{7} : \frac{21}{7}$ .
This simplifies to $5:3$ .
So for every 5 guitar players, there are 3 drummers.
Much easier to work with!

STEP 5

Now, we can set up a proportion to find the number of drummers.
We know the simplified ratio of guitar players to drummers is $5:3$ .
Let's use ' $d$ ' to represent the unknown number of drummers.

STEP 6

We can write the proportion as $\frac{\text{guitar players}}{\text{drummers}} = \frac{5}{3} = \frac{140}{d}$ .
We're putting the number of guitar players in the numerator and the number of drummers in the denominator on both sides of the equation.

STEP 7

Time to solve for $d$ !
We have the proportion $\frac{5}{3} = \frac{140}{d}$ .
To get $d$ by itself, we can cross-multiply.

STEP 8

Cross-multiplying gives us $5 \cdot d = 3 \cdot 140$ , which simplifies to $5d = 420$ .

STEP 9

Now, we want to isolate $d$ .
We can do this by dividing both sides of the equation by 5.
This gives us $\frac{5d}{5} = \frac{420}{5}$ .

STEP 10

So, $d = 84$ .
That means there are 84 drummers!

STEP 11

There are 84 drummers who tried out for the band.

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QuestionThe ratio of guitar players to drummers who tried out for a band is $35: 21$ . If there are 140 guitar players, how many drummers are there? label required

Studdy Solution

STEP 1

What is this asking? If we know the proportion of guitar players to drummers, and the total number of guitar players, how many drummers tried out? Watch out! Don't mix up the guitar players and drummers!
Keep track of which number goes with which instrument.

STEP 2

1. Simplify the Ratio
2. Set up a Proportion
3. Solve for the Number of Drummers

STEP 3

Alright, let's simplify that ratio of guitar players to drummers!
We've got $35:21$ .
Both of these numbers are divisible by 7.

STEP 4

Dividing both sides of the ratio by 7, we get $\frac{35}{7} : \frac{21}{7}$ .
This simplifies to $5:3$ .
So for every 5 guitar players, there are 3 drummers.
Much easier to work with!

STEP 5

Now, we can set up a proportion to find the number of drummers.
We know the simplified ratio of guitar players to drummers is $5:3$ .
Let's use ' $d$ ' to represent the unknown number of drummers.

STEP 6

We can write the proportion as $\frac{\text{guitar players}}{\text{drummers}} = \frac{5}{3} = \frac{140}{d}$ .
We're putting the number of guitar players in the numerator and the number of drummers in the denominator on both sides of the equation.

STEP 7

Time to solve for $d$ !
We have the proportion $\frac{5}{3} = \frac{140}{d}$ .
To get $d$ by itself, we can cross-multiply.

STEP 8

Cross-multiplying gives us $5 \cdot d = 3 \cdot 140$ , which simplifies to $5d = 420$ .

STEP 9

Now, we want to isolate $d$ .
We can do this by dividing both sides of the equation by 5.
This gives us $\frac{5d}{5} = \frac{420}{5}$ .

STEP 10

So, $d = 84$ .
That means there are 84 drummers!

STEP 11

There are 84 drummers who tried out for the band.

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QuestionThe ratio of guitar players to drummers who tried out for a band is 35:2135: 2135:21. If there are 140 guitar players, how many drummers are there? label required

Studdy Solution

STEP 1

What is this asking? If we know the proportion of guitar players to drummers, and the total number of guitar players, how many drummers tried out? Watch out! Don't mix up the guitar players and drummers!Keep track of which number goes with which instrument.

STEP 2

1. Simplify the Ratio2. Set up a Proportion3. Solve for the Number of Drummers

STEP 3

Alright, let's **simplify** that ratio of guitar players to drummers!We've got 35:2135:2135:21.Both of these numbers are divisible by **7**.

STEP 4

Dividing both sides of the ratio by **7**, we get 357:217\frac{35}{7} : \frac{21}{7}735​:721​.This simplifies to 5:35:35:3.So for every **5** guitar players, there are **3** drummers.Much easier to work with!

STEP 5

Now, we can **set up a proportion** to find the number of drummers.We know the simplified ratio of guitar players to drummers is 5:35:35:3.Let's use 'ddd' to represent the **unknown** number of drummers.

STEP 6

STEP 7

Time to **solve for** ddd!We have the proportion 53=140d\frac{5}{3} = \frac{140}{d}35​=d140​.To get ddd by itself, we can **cross-multiply**.

STEP 8

Cross-multiplying gives us 5⋅d=3⋅1405 \cdot d = 3 \cdot 1405⋅d=3⋅140, which simplifies to 5d=4205d = 4205d=420.

STEP 9

Now, we want to **isolate** ddd.We can do this by dividing both sides of the equation by **5**.This gives us 5d5=4205\frac{5d}{5} = \frac{420}{5}55d​=5420​.

STEP 10

So, d=84d = 84d=84.That means there are **84** drummers!

STEP 11

There are **84** drummers who tried out for the band.

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.

QuestionThe ratio of guitar players to drummers who tried out for a band is $35: 21$ . If there are 140 guitar players, how many drummers are there? label required

What is this asking? If we know the proportion of guitar players to drummers, and the total number of guitar players, how many drummers tried out? Watch out! Don't mix up the guitar players and drummers!
Keep track of which number goes with which instrument.

1. Simplify the Ratio
2. Set up a Proportion
3. Solve for the Number of Drummers

Alright, let's simplify that ratio of guitar players to drummers!
We've got $35:21$ .
Both of these numbers are divisible by 7.

Dividing both sides of the ratio by 7, we get $\frac{35}{7} : \frac{21}{7}$ .
This simplifies to $5:3$ .
So for every 5 guitar players, there are 3 drummers.
Much easier to work with!

Now, we can set up a proportion to find the number of drummers.
We know the simplified ratio of guitar players to drummers is $5:3$ .
Let's use ' $d$ ' to represent the unknown number of drummers.

Time to solve for $d$ !
We have the proportion $\frac{5}{3} = \frac{140}{d}$ .
To get $d$ by itself, we can cross-multiply.

Cross-multiplying gives us $5 \cdot d = 3 \cdot 140$ , which simplifies to $5d = 420$ .

Now, we want to isolate $d$ .
We can do this by dividing both sides of the equation by 5.
This gives us $\frac{5d}{5} = \frac{420}{5}$ .

So, $d = 84$ .
That means there are 84 drummers!

There are 84 drummers who tried out for the band.