Question 1

Solve.
-A bag of fertilizer covers 2000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 210 feet by 90 feet.

Accepted Answer

First, calculate the area of the lawn: 210 feet * 90 feet = 18,900 square feet. Then, divide by the area covered by one bag: 18,900 / 2,000 = 9.45. Since you can't purchase a fraction of a bag, round up to the nearest whole number, which is 10 bags.

Question 2

Solve.
-The ratio of a quarterback's completed passes to attempted passes is 2 to 3 . If he attempted 6 passes, find how many passes he completed. Round to the nearest whole number if necessary.

Accepted Answer

The ratio of completed to attempted passes is 2:3. If he attempted 6 passes, then the number of completed passes is (2/3) * 6 = 4 passes.

Question 3

Solve the proportion.
-$\frac { 1 } { x + 3 } = \frac { 3 } { 5 x }$

Accepted Answer

The answer of Solve the proportion.
-\(\frac { 1 } {...

Question 4

Solve.
-The ratio of the weight of an object on Earth to the weight of the same object on Pluto is 100 to 3 . If a buffalo weighs 3905 pounds on Earth, find the buffalo's weight on Pluto. (Round to the nearest pound.)

Accepted Answer

The weight of the buffalo on Pluto can be found by dividing its weight on Earth by the ratio of Earth's weight to Pluto's weight, which is 100/3. So, $3905 \div (100/3) = 117.15$, which rounds to 117 pounds.

Question 5

Solve.
-Three out of 10 adults in a certain city buy their drugs at large drug stores. If this city has 138,000 adults, how many of these adults would you expect to buy their drugs at large drug stores?

Accepted Answer

To find the number of adults buying drugs at large drug stores, multiply 138,000 by 3/10, which equals 41,400.

Question 6

Solve.
-The scale on a map states that 1 centimeter corresponds to 30 kilometers. On the map, two cities are $27 \mathrm {~cm}$ apart. Find the actual distance.

Accepted Answer

The actual distance is calculated by multiplying the map distance by the scale factor: $27 \mathrm {~cm} \times 30 \mathrm {~km/cm} = 810 \mathrm {~km}$.

Question 7

Solve.
-It is recommended that there be at least $9.3$ square feet of ground space in a garden for every newly planted shrub. A garden is $15.5$ feet by 18 feet. Find the maximum number of shrubs the garden can accommodate.

Accepted Answer

The area of the garden is $15.5 \times 18 = 279$ square feet. Dividing the total area by the space required per shrub, $279 \div 9.3 \approx 30$. Thus, the garden can accommodate a maximum of 30 shrubs.

Question 8

Solve.
-On an architect's blueprint, 1 inch corresponds to 12 feet. Find the length of a wall represented by a line $4 \frac { 1 } { 4 }$ inches long on the blueprint. Round to the nearest tenth if necessary.

Accepted Answer

To find the actual length of the wall, multiply the length of the line on the blueprint by the scale factor. $4 \frac { 1 } { 4 }$ inches is $4.25$ inches. Multiplying $4.25$ inches by $12$ feet/inch gives $51$ feet.

Question 9

Solve the proportion.
-$\frac { x + 5 } { x } = \frac { 2 } { 3 }$

Accepted Answer

To solve the proportion $\frac{x + 5}{x} = \frac{2}{3}$, cross-multiply to get $3(x + 5) = 2x$. This simplifies to $3x + 15 = 2x$, and by subtracting $2x$ from both sides, we get $x = -15$.

Question 10

Solve the proportion.
-$\frac { 10 } { x } = \frac { 5 } { 2 }$

Accepted Answer

Cross-multiply to get 10(2) = 5x. Divide both sides by 5 to get x = 4.

Question 11

Solve the proportion.
-$\frac { x + 6 } { 5 } = \frac { x + 8 } { 7 }$

Accepted Answer

To solve the proportion $\frac{x + 6}{5} = \frac{x + 8}{7}$, cross-multiply to get $7(x + 6) = 5(x + 8)$. Simplifying, $7x + 42 = 5x + 40$. Subtracting $5x$ and $42$ from both sides gives $2x = -2$, so $x = -1$.

Question 12

Solve.
-On an architect's blueprint, 1 inch corresponds to 4 feet. If an exterior wall is 12 feet long, find how long the blueprint measurement should be. Write answer as a mixed number if necessary.

Accepted Answer

The blueprint scale is 1 inch to 4 feet. For a 12 feet wall, the blueprint measurement is $12 \div 4 = 3$ inches.

Question 13

Solve the proportion.
-$\frac { 2 x + 3 } { x } = \frac { 3 } { 2 }$

Accepted Answer

Cross-multiply to get $4x + 6 = 3x$. Solving for $x$, we get $x = -6$.

Question 14

Solve.
-It is recommended that there be at least $11.1$ square feet of floor space in a classroom for every student in the class. Find the minimum floor space that 32 students require. Round to the nearest tenth if necessary.

Accepted Answer

To find the minimum floor space required for 32 students, multiply the number of students by the recommended square feet per student: $32 \times 11.1 = 355.2$ square feet.

Question 15

Solve.
-On a map of Nature's Wonder Hiking Trails, 1 centimeter corresponds to 3 miles. Find the length of a trail represented by a line that is $4 \frac { 1 } { 2 }$ centimeters long on the map.

Accepted Answer

To find the actual length of the trail, multiply the length of the line on the map by the scale factor. $4 \frac { 1 } { 2 } \text{ cm} \times 3 \text{ miles/cm} = 13 \frac { 1 } { 2 } \text{ miles}$.

Question 16

Solve the proportion.
-$\frac { 11 } { 6 } = \frac { x - 9 } { x - 5 }$

Accepted Answer

The answer of Solve the proportion.
-\(\frac { 11 } {...

Question 17

Solve.
-It is recommended that there be at least 17 square feet of work space for every person in a conference room. A certain conference room is 18 feet by 18 feet. Find the maximum number of people the room can accommodate.

Accepted Answer

The answer of Solve.
-It is recommended that there be at...

Question 18

Solve.
-The ratio of the weight of an object on Earth to an object on Planet $X$ is 3 to 11 . If a person weighs 150 pounds on Earth, find his weight on Planet X. (Round to the nearest whole number, if necessary.)

Accepted Answer

The weight ratio from Earth to Planet X is 3:11. To find the weight on Planet X, set up a proportion: $150 \text{ lb on Earth} \times \frac{11}{3} = 550 \text{ lb on Planet X}$.

Question 19

Solve.
-There are $1.1$ milligrams of iron in a $3.5$ ounce serving of chicken. How much iron is in 9 ounces of chicken? Round the answer to one decimal place.

Accepted Answer

To find the amount of iron in 9 ounces of chicken, set up a proportion: $ \frac{1.1 \, \text{mg}}{3.5 \, \text{oz}} = \frac{x \, \text{mg}}{9 \, \text{oz}} $. Solving for $ x $ gives $ x = \frac{1.1 \times 9}{3.5} = 2.8 \, \text{mg} $.

Question 20

Solve the proportion.
-$\frac { 9 } { 8 } = \frac { 2 x } { 7 }$

Accepted Answer

To solve the proportion, cross-multiply to get $9 \times 7 = 8 \times 2x$. Simplifying gives $63 = 16x$, so $x = \frac{63}{16}$.

Quiz 7: Rational Expressions

Solve. -A bag of fertilizer covers 2000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 210 feet by 90 feet.

Solve. -The ratio of a quarterback's completed passes to attempted passes is 2 to 3 . If he attempted 6 passes, find how many passes he completed. Round to the nearest whole number if necessary.

Solve the proportion. - $\frac { 1 } { x + 3 } = \frac { 3 } { 5 x }$

Solve. -The ratio of the weight of an object on Earth to the weight of the same object on Pluto is 100 to 3 . If a buffalo weighs 3905 pounds on Earth, find the buffalo's weight on Pluto. (Round to the nearest pound.)

Solve. -Three out of 10 adults in a certain city buy their drugs at large drug stores. If this city has 138,000 adults, how many of these adults would you expect to buy their drugs at large drug stores?

Solve. -The scale on a map states that 1 centimeter corresponds to 30 kilometers. On the map, two cities are $27 \mathrm {~cm}$ apart. Find the actual distance.

Solve. -It is recommended that there be at least $9.3$ square feet of ground space in a garden for every newly planted shrub. A garden is $15.5$ feet by 18 feet. Find the maximum number of shrubs the garden can accommodate.

Solve. -On an architect's blueprint, 1 inch corresponds to 12 feet. Find the length of a wall represented by a line $4 \frac { 1 } { 4 }$ inches long on the blueprint. Round to the nearest tenth if necessary.

Solve the proportion. - $\frac { x + 5 } { x } = \frac { 2 } { 3 }$

Solve the proportion. - $\frac { 10 } { x } = \frac { 5 } { 2 }$

Solve the proportion. - $\frac { x + 6 } { 5 } = \frac { x + 8 } { 7 }$

Solve. -On an architect's blueprint, 1 inch corresponds to 4 feet. If an exterior wall is 12 feet long, find how long the blueprint measurement should be. Write answer as a mixed number if necessary.

Solve the proportion. - $\frac { 2 x + 3 } { x } = \frac { 3 } { 2 }$

Solve. -It is recommended that there be at least $11.1$ square feet of floor space in a classroom for every student in the class. Find the minimum floor space that 32 students require. Round to the nearest tenth if necessary.

Solve. -On a map of Nature's Wonder Hiking Trails, 1 centimeter corresponds to 3 miles. Find the length of a trail represented by a line that is $4 \frac { 1 } { 2 }$ centimeters long on the map.

Solve the proportion. - $\frac { 11 } { 6 } = \frac { x - 9 } { x - 5 }$

Solve. -It is recommended that there be at least 17 square feet of work space for every person in a conference room. A certain conference room is 18 feet by 18 feet. Find the maximum number of people the room can accommodate.

Solve. -The ratio of the weight of an object on Earth to an object on Planet $X$ is 3 to 11 . If a person weighs 150 pounds on Earth, find his weight on Planet X. (Round to the nearest whole number, if necessary.)

Solve. -There are $1.1$ milligrams of iron in a $3.5$ ounce serving of chicken. How much iron is in 9 ounces of chicken? Round the answer to one decimal place.

Solve the proportion. - $\frac { 9 } { 8 } = \frac { 2 x } { 7 }$

Quiz 7: Rational Expressions

Solve. -A bag of fertilizer covers 2000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 210 feet by 90 feet.

Solve. -The ratio of a quarterback's completed passes to attempted passes is 2 to 3 . If he attempted 6 passes, find how many passes he completed. Round to the nearest whole number if necessary.

Solve the proportion. - 1x+3=35x\frac { 1 } { x + 3 } = \frac { 3 } { 5 x }x+31​=5x3​

Solve. -The ratio of the weight of an object on Earth to the weight of the same object on Pluto is 100 to 3 . If a buffalo weighs 3905 pounds on Earth, find the buffalo's weight on Pluto. (Round to the nearest pound.)

Solve. -Three out of 10 adults in a certain city buy their drugs at large drug stores. If this city has 138,000 adults, how many of these adults would you expect to buy their drugs at large drug stores?

Solve. -The scale on a map states that 1 centimeter corresponds to 30 kilometers. On the map, two cities are 27 cm27 \mathrm {~cm}27 cm apart. Find the actual distance.

Solve. -It is recommended that there be at least 9.39.39.3 square feet of ground space in a garden for every newly planted shrub. A garden is 15.515.515.5 feet by 18 feet. Find the maximum number of shrubs the garden can accommodate.

Solve. -On an architect's blueprint, 1 inch corresponds to 12 feet. Find the length of a wall represented by a line 4144 \frac { 1 } { 4 }441​ inches long on the blueprint. Round to the nearest tenth if necessary.

Solve the proportion. - x+5x=23\frac { x + 5 } { x } = \frac { 2 } { 3 }xx+5​=32​

Solve the proportion. - 10x=52\frac { 10 } { x } = \frac { 5 } { 2 }x10​=25​

Solve the proportion. - x+65=x+87\frac { x + 6 } { 5 } = \frac { x + 8 } { 7 }5x+6​=7x+8​

Solve. -On an architect's blueprint, 1 inch corresponds to 4 feet. If an exterior wall is 12 feet long, find how long the blueprint measurement should be. Write answer as a mixed number if necessary.

Solve the proportion. - 2x+3x=32\frac { 2 x + 3 } { x } = \frac { 3 } { 2 }x2x+3​=23​

Solve. -It is recommended that there be at least 11.111.111.1 square feet of floor space in a classroom for every student in the class. Find the minimum floor space that 32 students require. Round to the nearest tenth if necessary.

Solve. -On a map of Nature's Wonder Hiking Trails, 1 centimeter corresponds to 3 miles. Find the length of a trail represented by a line that is 4124 \frac { 1 } { 2 }421​ centimeters long on the map.

Solve the proportion. - 116=x−9x−5\frac { 11 } { 6 } = \frac { x - 9 } { x - 5 }611​=x−5x−9​