Math / Numbers & Operations

Question14. In the high school band there are 2 percussionists on the sideline to every 13 marching instruments. If the high school band has 150 total members, then how many percussionists are on the sideline? Find the scale factor and use it to solve.

Studdy Solution

STEP 1

1. The ratio of percussionists on the sideline to marching instruments is $2$ to $13$ .
2. The total number of band members is $150$ .
3. We need to find the number of percussionists on the sideline.
4. The scale factor will help us determine the number of percussionists.

STEP 2

1. Define the variables.
2. Set up the equation using the ratio.
3. Find the scale factor.
4. Use the scale factor to find the number of percussionists.

STEP 3

Let $p$ be the number of percussionists on the sideline, and let $m$ be the number of marching instruments.

STEP 4

Use the given ratio to express the relationship between percussionists and marching instruments.
$\frac{p}{m} = \frac{2}{13}$

STEP 5

Express the total number of band members in terms of $p$ and $m$ .
$p + m = 150$

STEP 6

Substitute $m = \frac{13}{2}p$ into the total member equation.
$p + \frac{13}{2}p = 150$

STEP 7

Combine the terms and solve for $p$ .
$\frac{2}{2}p + \frac{13}{2}p = 150$ $\frac{15}{2}p = 150$

STEP 8

Multiply both sides by $\frac{2}{15}$ to solve for $p$ .
$p = 150 \times \frac{2}{15}$ $p = 20$

STEP 9

The scale factor is the ratio of the total number of band members to the sum of the parts of the ratio.
$\text{Scale factor} = \frac{150}{15} = 10$

STEP 10

Use the scale factor to verify the number of percussionists.
$p = 2 \times 10 = 20$
The number of percussionists on the sideline is:
$\boxed{20}$

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Question14. In the high school band there are 2 percussionists on the sideline to every 13 marching instruments. If the high school band has 150 total members, then how many percussionists are on the sideline? Find the scale factor and use it to solve.

Studdy Solution

STEP 1

1. The ratio of percussionists on the sideline to marching instruments is $2$ to $13$ .
2. The total number of band members is $150$ .
3. We need to find the number of percussionists on the sideline.
4. The scale factor will help us determine the number of percussionists.

STEP 2

1. Define the variables.
2. Set up the equation using the ratio.
3. Find the scale factor.
4. Use the scale factor to find the number of percussionists.

STEP 3

Let $p$ be the number of percussionists on the sideline, and let $m$ be the number of marching instruments.

STEP 4

Use the given ratio to express the relationship between percussionists and marching instruments.
$\frac{p}{m} = \frac{2}{13}$

STEP 5

Express the total number of band members in terms of $p$ and $m$ .
$p + m = 150$

STEP 6

Substitute $m = \frac{13}{2}p$ into the total member equation.
$p + \frac{13}{2}p = 150$

STEP 7

Combine the terms and solve for $p$ .
$\frac{2}{2}p + \frac{13}{2}p = 150$ $\frac{15}{2}p = 150$

STEP 8

Multiply both sides by $\frac{2}{15}$ to solve for $p$ .
$p = 150 \times \frac{2}{15}$ $p = 20$

STEP 9

The scale factor is the ratio of the total number of band members to the sum of the parts of the ratio.
$\text{Scale factor} = \frac{150}{15} = 10$

STEP 10

Use the scale factor to verify the number of percussionists.
$p = 2 \times 10 = 20$
The number of percussionists on the sideline is:
$\boxed{20}$

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Question14. In the high school band there are 2 percussionists on the sideline to every 13 marching instruments. If the high school band has 150 total members, then how many percussionists are on the sideline? Find the scale factor and use it to solve.

Studdy Solution

STEP 1

1. The ratio of percussionists on the sideline to marching instruments is 2 2 2 to 13 13 13.2. The total number of band members is 150 150 150.3. We need to find the number of percussionists on the sideline.4. The scale factor will help us determine the number of percussionists.

STEP 2

1. Define the variables.2. Set up the equation using the ratio.3. Find the scale factor.4. Use the scale factor to find the number of percussionists.

STEP 3

Let p p p be the number of percussionists on the sideline, and let m m m be the number of marching instruments.

STEP 4

Use the given ratio to express the relationship between percussionists and marching instruments.pm=213\frac{p}{m} = \frac{2}{13}mp​=132​

STEP 5

Express the total number of band members in terms of p p p and m m m.p+m=150p + m = 150p+m=150

STEP 6

Substitute m=132p m = \frac{13}{2}p m=213​p into the total member equation.p+132p=150p + \frac{13}{2}p = 150p+213​p=150

STEP 7

Combine the terms and solve for p p p.22p+132p=150\frac{2}{2}p + \frac{13}{2}p = 15022​p+213​p=150 152p=150\frac{15}{2}p = 150215​p=150

STEP 8

Multiply both sides by 215 \frac{2}{15} 152​ to solve for p p p.p=150×215p = 150 \times \frac{2}{15}p=150×152​ p=20p = 20p=20

STEP 9

The scale factor is the ratio of the total number of band members to the sum of the parts of the ratio.Scale factor=15015=10\text{Scale factor} = \frac{150}{15} = 10Scale factor=15150​=10

STEP 10

Use the scale factor to verify the number of percussionists.p=2×10=20p = 2 \times 10 = 20p=2×10=20 The number of percussionists on the sideline is:20\boxed{20}20​

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1. The ratio of percussionists on the sideline to marching instruments is $2$ to $13$ .
2. The total number of band members is $150$ .
3. We need to find the number of percussionists on the sideline.
4. The scale factor will help us determine the number of percussionists.

1. Define the variables.
2. Set up the equation using the ratio.
3. Find the scale factor.
4. Use the scale factor to find the number of percussionists.

Let $p$ be the number of percussionists on the sideline, and let $m$ be the number of marching instruments.

Use the given ratio to express the relationship between percussionists and marching instruments.
$\frac{p}{m} = \frac{2}{13}$

Express the total number of band members in terms of $p$ and $m$ .
$p + m = 150$

Substitute $m = \frac{13}{2}p$ into the total member equation.
$p + \frac{13}{2}p = 150$

Combine the terms and solve for $p$ .
$\frac{2}{2}p + \frac{13}{2}p = 150$ $\frac{15}{2}p = 150$

Multiply both sides by $\frac{2}{15}$ to solve for $p$ .
$p = 150 \times \frac{2}{15}$ $p = 20$

The scale factor is the ratio of the total number of band members to the sum of the parts of the ratio.
$\text{Scale factor} = \frac{150}{15} = 10$

Use the scale factor to verify the number of percussionists.
$p = 2 \times 10 = 20$
The number of percussionists on the sideline is:
$\boxed{20}$