Math / Numbers & Operations

Question1. Holsteins to Jersey
4. Holsteins to non-Holsteins
5. Holsteins to
Express the answers to the following questions in lowest terms using the word "to."
1. A school has 2,600 students and 104 teachers. What is the student-to-teacher ratio?
8. A store has 10 departments and 48 employees. What is
9. A department store ordered 80 regular-length sular lengths to talls? regular lengths to both other lengths combined? regular
10. Some concrete was mixed using 550 lb . of cement and $1,650 \mathrm{lb}$ , of sand. What was the ratio of cement to sand?
11. If concrete is mixed using $1,650 \mathrm{lb}$ . of sand and 330 lb . of water, what is the ratio of sand to water?
12. Mr. and Mrs. Jackson have fourteen grandchildren. Find the ratio of girls to boys if there are four more girls than boys.

Studdy Solution

STEP 1

1. Ratios are expressed in the form "A to B."
2. All given quantities are whole numbers.
3. Ratios should be simplified to their lowest terms.

STEP 2

1. Calculate the student-to-teacher ratio.
2. Calculate the department-to-employee ratio.
3. Calculate the regular-length to other lengths ratio.
4. Calculate the cement-to-sand ratio.
5. Calculate the sand-to-water ratio.
6. Calculate the girls-to-boys ratio.

STEP 3

Calculate the student-to-teacher ratio.
$\text{Student-to-teacher ratio} = \frac{2600}{104}$
Simplify the fraction:
$\frac{2600}{104} = \frac{25}{1}$
The student-to-teacher ratio is $25 \text{ to } 1$ .

STEP 4

Calculate the department-to-employee ratio.
$\text{Department-to-employee ratio} = \frac{10}{48}$
Simplify the fraction:
$\frac{10}{48} = \frac{5}{24}$
The department-to-employee ratio is $5 \text{ to } 24$ .

STEP 5

Calculate the regular-length to other lengths ratio.
Given: Regular lengths = 80, Total lengths = 80 + 48 + 10 = 138
Other lengths = Total lengths - Regular lengths = 138 - 80 = 58
$\text{Regular-length to other lengths ratio} = \frac{80}{58}$
Simplify the fraction:
$\frac{80}{58} = \frac{40}{29}$
The regular-length to other lengths ratio is $40 \text{ to } 29$ .

STEP 6

Calculate the cement-to-sand ratio.
$\text{Cement-to-sand ratio} = \frac{550}{1650}$
Simplify the fraction:
$\frac{550}{1650} = \frac{1}{3}$
The cement-to-sand ratio is $1 \text{ to } 3$ .

STEP 7

Calculate the sand-to-water ratio.
$\text{Sand-to-water ratio} = \frac{1650}{330}$
Simplify the fraction:
$\frac{1650}{330} = \frac{5}{1}$
The sand-to-water ratio is $5 \text{ to } 1$ .

STEP 8

Calculate the girls-to-boys ratio.
Let $b$ be the number of boys. Then, the number of girls is $b + 4$ .
Total grandchildren = 14
$b + (b + 4) = 14$
$2b + 4 = 14$
$2b = 10$
$b = 5$
Number of girls = $b + 4 = 9$
Girls-to-boys ratio:
$\frac{9}{5}$
The girls-to-boys ratio is $9 \text{ to } 5$ .

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Studdy Solution

STEP 1

1. Ratios are expressed in the form "A to B."
2. All given quantities are whole numbers.
3. Ratios should be simplified to their lowest terms.

STEP 2

1. Calculate the student-to-teacher ratio.
2. Calculate the department-to-employee ratio.
3. Calculate the regular-length to other lengths ratio.
4. Calculate the cement-to-sand ratio.
5. Calculate the sand-to-water ratio.
6. Calculate the girls-to-boys ratio.

STEP 3

Calculate the student-to-teacher ratio.
$\text{Student-to-teacher ratio} = \frac{2600}{104}$
Simplify the fraction:
$\frac{2600}{104} = \frac{25}{1}$
The student-to-teacher ratio is $25 \text{ to } 1$ .

STEP 4

Calculate the department-to-employee ratio.
$\text{Department-to-employee ratio} = \frac{10}{48}$
Simplify the fraction:
$\frac{10}{48} = \frac{5}{24}$
The department-to-employee ratio is $5 \text{ to } 24$ .

STEP 5

STEP 6

Calculate the cement-to-sand ratio.
$\text{Cement-to-sand ratio} = \frac{550}{1650}$
Simplify the fraction:
$\frac{550}{1650} = \frac{1}{3}$
The cement-to-sand ratio is $1 \text{ to } 3$ .

STEP 7

Calculate the sand-to-water ratio.
$\text{Sand-to-water ratio} = \frac{1650}{330}$
Simplify the fraction:
$\frac{1650}{330} = \frac{5}{1}$
The sand-to-water ratio is $5 \text{ to } 1$ .

STEP 8

Calculate the girls-to-boys ratio.
Let $b$ be the number of boys. Then, the number of girls is $b + 4$ .
Total grandchildren = 14
$b + (b + 4) = 14$
$2b + 4 = 14$
$2b = 10$
$b = 5$
Number of girls = $b + 4 = 9$
Girls-to-boys ratio:
$\frac{9}{5}$
The girls-to-boys ratio is $9 \text{ to } 5$ .

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Studdy Solution

STEP 1

1. Ratios are expressed in the form "A to B."2. All given quantities are whole numbers.3. Ratios should be simplified to their lowest terms.

STEP 2

1. Calculate the student-to-teacher ratio.2. Calculate the department-to-employee ratio.3. Calculate the regular-length to other lengths ratio.4. Calculate the cement-to-sand ratio.5. Calculate the sand-to-water ratio.6. Calculate the girls-to-boys ratio.

STEP 3

STEP 4

STEP 5

STEP 6

Calculate the cement-to-sand ratio.Cement-to-sand ratio=5501650\text{Cement-to-sand ratio} = \frac{550}{1650}Cement-to-sand ratio=1650550​Simplify the fraction:5501650=13\frac{550}{1650} = \frac{1}{3}1650550​=31​The cement-to-sand ratio is 1 to 3 1 \text{ to } 3 1 to 3.

STEP 7

Calculate the sand-to-water ratio.Sand-to-water ratio=1650330\text{Sand-to-water ratio} = \frac{1650}{330}Sand-to-water ratio=3301650​Simplify the fraction:1650330=51\frac{1650}{330} = \frac{5}{1}3301650​=15​The sand-to-water ratio is 5 to 1 5 \text{ to } 1 5 to 1.

STEP 8

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1. Ratios are expressed in the form "A to B."
2. All given quantities are whole numbers.
3. Ratios should be simplified to their lowest terms.

1. Calculate the student-to-teacher ratio.
2. Calculate the department-to-employee ratio.
3. Calculate the regular-length to other lengths ratio.
4. Calculate the cement-to-sand ratio.
5. Calculate the sand-to-water ratio.
6. Calculate the girls-to-boys ratio.

Calculate the cement-to-sand ratio.
$\text{Cement-to-sand ratio} = \frac{550}{1650}$
Simplify the fraction:
$\frac{550}{1650} = \frac{1}{3}$
The cement-to-sand ratio is $1 \text{ to } 3$ .

Calculate the sand-to-water ratio.
$\text{Sand-to-water ratio} = \frac{1650}{330}$
Simplify the fraction:
$\frac{1650}{330} = \frac{5}{1}$
The sand-to-water ratio is $5 \text{ to } 1$ .