Math / Algebra

QuestionThe ratio of red to blue marbles in a bowl is $7: 8$ . There are 30 marbles total. How many red and blue marbles are there? A. 7 red and 8 blue B. 8 red and 7 blue C. 10 red and 12 blue D. 14 red and 16 blue

Studdy Solution

STEP 1

What is this asking? If we have a bunch of marbles, some red and some blue, and we know the ratio of red to blue marbles and the total number of marbles, how many of each color are there? Watch out! Don't just pick the answer with the right ratio!
We need to make sure the total number of marbles matches what's given in the problem.

STEP 2

1. Find the total number of "parts" in the ratio.
2. Calculate the value of one "part".
3. Determine the number of red marbles.
4. Determine the number of blue marbles.

STEP 3

The ratio $7:8$ means that for every 7 red marbles, we have 8 blue marbles.
Think of it like this: we have 7 "parts" of red marbles and 8 "parts" of blue marbles.

STEP 4

To find the total number of "parts," we add the number of red "parts" and the number of blue "parts": $7 + 8 = \mathbf{15}$ .
So, there are a total of 15 "parts."

STEP 5

We know that there are 30 total marbles, and these 30 marbles are divided into 15 equal "parts."

STEP 6

To find the value of one "part," we divide the total number of marbles by the total number of "parts": $30 \div 15 = \mathbf{2}$ .
So, one "part" represents 2 marbles.

STEP 7

The ratio tells us that there are 7 "parts" of red marbles.

STEP 8

Since one "part" is 2 marbles, we multiply the number of red "parts" by the value of one "part" to get the number of red marbles: $7 \cdot 2 = \mathbf{14}$ red marbles.

STEP 9

The ratio tells us that there are 8 "parts" of blue marbles.

STEP 10

Since one "part" is 2 marbles, we multiply the number of blue "parts" by the value of one "part" to get the number of blue marbles: $8 \cdot 2 = \mathbf{16}$ blue marbles.

STEP 11

There are 14 red marbles and 16 blue marbles.
This makes 30 marbles in total, and a ratio of $14:16$ , which simplifies to $7:8$ , as expected!
The correct answer is D.

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QuestionThe ratio of red to blue marbles in a bowl is $7: 8$ . There are 30 marbles total. How many red and blue marbles are there? A. 7 red and 8 blue B. 8 red and 7 blue C. 10 red and 12 blue D. 14 red and 16 blue

Studdy Solution

STEP 1

STEP 2

1. Find the total number of "parts" in the ratio.
2. Calculate the value of one "part".
3. Determine the number of red marbles.
4. Determine the number of blue marbles.

STEP 3

The ratio $7:8$ means that for every 7 red marbles, we have 8 blue marbles.
Think of it like this: we have 7 "parts" of red marbles and 8 "parts" of blue marbles.

STEP 4

To find the total number of "parts," we add the number of red "parts" and the number of blue "parts": $7 + 8 = \mathbf{15}$ .
So, there are a total of 15 "parts."

STEP 5

We know that there are 30 total marbles, and these 30 marbles are divided into 15 equal "parts."

STEP 6

To find the value of one "part," we divide the total number of marbles by the total number of "parts": $30 \div 15 = \mathbf{2}$ .
So, one "part" represents 2 marbles.

STEP 7

The ratio tells us that there are 7 "parts" of red marbles.

STEP 8

Since one "part" is 2 marbles, we multiply the number of red "parts" by the value of one "part" to get the number of red marbles: $7 \cdot 2 = \mathbf{14}$ red marbles.

STEP 9

The ratio tells us that there are 8 "parts" of blue marbles.

STEP 10

Since one "part" is 2 marbles, we multiply the number of blue "parts" by the value of one "part" to get the number of blue marbles: $8 \cdot 2 = \mathbf{16}$ blue marbles.

STEP 11

There are 14 red marbles and 16 blue marbles.
This makes 30 marbles in total, and a ratio of $14:16$ , which simplifies to $7:8$ , as expected!
The correct answer is D.

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QuestionThe ratio of red to blue marbles in a bowl is 7:87: 87:8. There are 30 marbles total. How many red and blue marbles are there? A. 7 red and 8 blue B. 8 red and 7 blue C. 10 red and 12 blue D. 14 red and 16 blue

Studdy Solution

STEP 1

STEP 2

1. Find the total number of "parts" in the ratio.2. Calculate the value of one "part".3. Determine the number of red marbles.4. Determine the number of blue marbles.

STEP 3

The ratio 7:87:87:8 means that for every **7** red marbles, we have **8** blue marbles.Think of it like this: we have **7** "parts" of red marbles and **8** "parts" of blue marbles.

STEP 4

To find the total number of "parts," we add the number of red "parts" and the number of blue "parts": 7+8=157 + 8 = \mathbf{15}7+8=15.So, there are a total of **15** "parts."

STEP 5

We know that there are **30** total marbles, and these **30** marbles are divided into **15** equal "parts."

STEP 6

To find the value of one "part," we divide the total number of marbles by the total number of "parts": 30÷15=230 \div 15 = \mathbf{2}30÷15=2.So, one "part" represents **2** marbles.

STEP 7

The ratio tells us that there are **7** "parts" of red marbles.

STEP 8

Since one "part" is **2** marbles, we multiply the number of red "parts" by the value of one "part" to get the number of red marbles: 7⋅2=147 \cdot 2 = \mathbf{14}7⋅2=14 red marbles.

STEP 9

The ratio tells us that there are **8** "parts" of blue marbles.

STEP 10

Since one "part" is **2** marbles, we multiply the number of blue "parts" by the value of one "part" to get the number of blue marbles: 8⋅2=168 \cdot 2 = \mathbf{16}8⋅2=16 blue marbles.

STEP 11

There are **14** red marbles and **16** blue marbles.This makes **30** marbles in total, and a ratio of 14:1614:1614:16, which simplifies to 7:87:87:8, as expected!The correct answer is D.

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QuestionThe ratio of red to blue marbles in a bowl is $7: 8$ . There are 30 marbles total. How many red and blue marbles are there? A. 7 red and 8 blue B. 8 red and 7 blue C. 10 red and 12 blue D. 14 red and 16 blue

1. Find the total number of "parts" in the ratio.
2. Calculate the value of one "part".
3. Determine the number of red marbles.
4. Determine the number of blue marbles.

The ratio $7:8$ means that for every 7 red marbles, we have 8 blue marbles.
Think of it like this: we have 7 "parts" of red marbles and 8 "parts" of blue marbles.

To find the total number of "parts," we add the number of red "parts" and the number of blue "parts": $7 + 8 = \mathbf{15}$ .
So, there are a total of 15 "parts."

We know that there are 30 total marbles, and these 30 marbles are divided into 15 equal "parts."

To find the value of one "part," we divide the total number of marbles by the total number of "parts": $30 \div 15 = \mathbf{2}$ .
So, one "part" represents 2 marbles.

The ratio tells us that there are 7 "parts" of red marbles.

Since one "part" is 2 marbles, we multiply the number of red "parts" by the value of one "part" to get the number of red marbles: $7 \cdot 2 = \mathbf{14}$ red marbles.

The ratio tells us that there are 8 "parts" of blue marbles.

Since one "part" is 2 marbles, we multiply the number of blue "parts" by the value of one "part" to get the number of blue marbles: $8 \cdot 2 = \mathbf{16}$ blue marbles.

There are 14 red marbles and 16 blue marbles.
This makes 30 marbles in total, and a ratio of $14:16$ , which simplifies to $7:8$ , as expected!
The correct answer is D.