Question 1

For the proportion, find the unknown number n.
-$\frac { \mathrm { n } } { \frac { 11 } { 13 } } = \frac { 2 \frac { 1 } { 6 } } { 1 \frac { 1 } { 10 } }$

Accepted Answer

To solve for n, first convert the mixed numbers to improper fractions: $2 \frac{1}{6} = \frac{13}{6}$ and $1 \frac{1}{10} = \frac{11}{10}$. The right side of the equation becomes $\frac{13}{6} \div \frac{11}{10} = \frac{13}{6} \times \frac{10}{11} = \frac{130}{66} = \frac{65}{33}$. The left side is $\frac{n}{\frac{11}{13}} = n \times \frac{13}{11}$. Equating both sides gives $n \times \frac{13}{11} = \frac{65}{33}$. Solving for n, $n = \frac{65}{33} \times \frac{11}{13} = \frac{65 \times 11}{33 \times 13} = \frac{715}{429} = \frac{65}{39} = 1 \frac{2}{3}$.

Question 2

Solve.
-One pound of a product yieldsds $2 \frac { 1 } { 4 }$ cups. How many pounds of this product will be required by a recipe that calls for 6 cups of the product?

Accepted Answer

To find out how many pounds are needed for 6 cups, divide 6 cups by the number of cups yielded per pound, which is $2 \frac{1}{4}$ or $2.25$. So, $6 \div 2.25 = 2.666...$, which simplifies to $2 \frac{2}{3}$ pounds.

Question 3

Solve.
-There are 0.5 milligrams of iron in a 3.5 ounce serving of cod. How much iron is in 4 ounces of cod? Round the answer to one decimal place.

Accepted Answer

To find out how much iron is in 4 ounces of cod, we set up a proportion based on the information given: 0.5 mg of iron is to 3.5 ounces of cod as X mg of iron is to 4 ounces of cod. Solving for X gives us X = (0.5 mg / 3.5 oz) * 4 oz = 0.5714 mg, which rounds to 0.6 mg.

Question 4

Solve.
-The ratio of a quarterback's completed passes to attempted passes is 7 to 8. If he attempted 16 passes, find how many passes he completed. Round to the nearest whole number if necessary.

Accepted Answer

If the ratio of completed passes to attempted passes is 7 to 8, this means that for every 7 completed passes, there were 8 attempted passes. 
We can set up a proportion:

completed passes/attempted passes = 7/8

Let x be the number of completed passes:

x/16 = 7/8

Solving for x, we get:

x = (7/8) * 16

x = 14

Therefore, the quarterback completed 14 passes. We can set up a proportion to solve for the number of passes completed (let x be the number of passes completed):

completed/attempted = 7/8

x/16 = 7/8

Cross-multiplying:

8x = 112

Dividing by 8:

x = 14

Therefore, the quarterback completed 14 passes.

Question 5

Solve.
-On an architect's blueprint, 1 inch corresponds to 8 feet. Find the length of a wall represented by a lineine $5 \frac { 1 } { 4 }$ inches long on the blueprint. Round to the nearest tenth if necessary.

Accepted Answer

1 inch corresponds to 8 feet. So, $5 \frac { 1 } { 4 }$ inches corresponds to $5 \frac { 1 } { 4 } \times 8 = 42$ feet.

Question 6

For the proportion, find the unknown number n.
-$\frac { \mathrm { n } } { 10 } = \frac { 1 } { 2 \frac { 1 } { 2 } }$

Accepted Answer

The answer of For the proportion, find the unknown number...

Question 7

For the proportion, find the unknown number n.
-$\frac { 3 } { \frac { 1 } { 6 } } = \frac { 18 } { n }$

Accepted Answer

The answer of For the proportion, find the unknown number...

Question 8

Solve.
-The scale on a map states that 1 centimeter corresponds to 30 kilometers. On the map, two cities are 0.7 cm apart. Find the actual distance.

Accepted Answer

The actual distance is found by multiplying the map distance by the scale factor: 0.7 cm * 30 km/cm = 21 km.

Question 9

For the proportion, find the unknown number n.
-$\frac { \frac { 1 } { 3 } } { \frac { 3 } { 9 } } = \frac { 17 } { n }$

Accepted Answer

The answer of For the proportion, find the unknown number...

Question 10

Solve.
-On an architect's blueprint, 1 inch corresponds to 4 feet. If an exterior wall is 24 feet long, find how long the blueprint measurement should be. Write answer as a mixed number if necessary.

Accepted Answer

The scale is 1 inch = 4 feet. For a 24-foot wall, divide 24 by 4 to convert to inches on the blueprint: 24 ÷ 4 = 6 inches.

Question 11

Solve.
-The ratio of a basketball player's completed free throws to attempted free throws is 5 to 6. If she completed 20 free throws, find how many free throws she attempted. Round to the nearest whole number if necessary.

Accepted Answer

The ratio of completed free throws : attempted free throws is given as 5:6.
Let's assume she attempted x free throws.
So, the ratio becomes completed free throws : attempted free throws = 5x : 6x
It is given that she completed 20 free throws.
Therefore, 5x = 20
=> x = 4
Hence, she attempted 6x = 6*4 = 24 free throws. If the ratio of completed free throws to attempted free throws is 5 to 6, then we can set up a proportion:

5/6 = 20/x (where x is the number of attempted free throws)

To solve for x, we can cross-multiply:

5x = 120

x = 24

Therefore, the basketball player attempted 24 free throws.

Question 12

Solve.
-It takes Winnie 22 minutes to word process and spell check 10 pages. Find how long it takes her to word process and spell check 45 pages. Round answers to the nearest whole number if necessary.

Accepted Answer

We can solve this using ratio and proportion. Let x be the time it takes Winnie to word process and spell check 45 pages.

We know that:

10 pages take 22 minutes

So, we can set up a proportion:

10/22 = 45/x

Cross-multiplying, we get:

10x = 22 * 45

Simplifying:

10x = 990

x = 99

Therefore, it will take Winnie 99 minutes to word process and spell check 45 pages. So, the answer is D. We can use proportions to solve the problem. Let's call the time it takes Winnie to word process and spell check 45 pages "t". Then we can set up the proportion:

10/22 = 45/t

To solve for t, we can cross-multiply and simplify:

10t = 22 * 45

10t = 990

t = 99

So it will take Winnie 99 minutes to word process and spell check 45 pages. Therefore, the best choice is D.

Question 13

For the proportion, find the unknown number n.
-$\frac { 0.6 } { 4.2 } = \frac { 5 } { n }$

Accepted Answer

The answer of For the proportion, find the unknown number...

Question 14

Solve.
-A baseball player makes 4 hits in every 7 times at bat. At this rate, if he made 24 hits, find how many times he batted.

Accepted Answer

The player makes 4 hits in every 7 times at bat. To find out how many times he batted for 24 hits, set up a proportion: 4 hits / 7 at-bats = 24 hits / x at-bats. Solving for x gives x = (24 * 7) / 4 = 42 times at bat.

Question 15

Solve.
-A punch recipe calls for mixing 6 parts of grape juice with 7 parts of lemon juice. Find how much grape juice should be mixed with 126 ounces of lemon juice.

Accepted Answer

The answer of Solve.
-A punch recipe calls for mixing 6...

Question 16

For the proportion, find the unknown number n.
-$\frac { 8.4 } { 14 } = \frac { n } { 2.8 }$

Accepted Answer

To solve for $n$, cross-multiply the proportions: $8.4 \times 2.8 = 14 \times n$. Simplifying gives $23.52 = 14n$. Dividing both sides by 14 gives $n = 1.68$.

Question 17

Solve.
-A can of lemonade comes with a measuring scoop and directions for mixing are 8 scoops of mix for every 24 cups of water. How much water is needed to make the entire can of lemonade if there are 40 scoops of mix?

Accepted Answer

The ratio of scoops of mix to cups of water is 8 scoops for every 24 cups of water. To find out how much water is needed for 40 scoops, set up a proportion: 8 scoops/24 cups = 40 scoops/x cups. Solving for x gives x = (40 scoops * 24 cups) / 8 scoops = 120 cups.

Question 18

For the proportion, find the unknown number n.
-$\frac { 294 } { 62 } = \frac { n } { 558 }$

Accepted Answer

To find the unknown number $n$, we can cross-multiply the given proportion: $294 \times 558 = 62 \times n$. Solving for $n$ gives $n = \frac{294 \times 558}{62} = 2646$.

Question 19

Solve.
-It takes Frank 10 minutes to word process and spell check 6 pages. Find how many pages he can word process and spell check in 0.5 hours. Round answers to the nearest tenth if necessary.

Accepted Answer

The answer of Solve.
-It takes Frank 10 minutes to word...

Question 20

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 160 feet by 120 feet.

Accepted Answer

To find the total area of the lawn, we use the formula: 
Area = length × width
Area = 160 feet × 120 feet
Area = 19200 square feet
To cover this area, we need to purchase:
Number of bags = Total area ÷ Area covered by one bag
Number of bags = 19200 ÷ 2000
Number of bags = 9.6
Since we cannot purchase a fraction of a bag, we need to round up to the nearest whole number. Therefore, we need to purchase 10 bags of fertilizer. The area of the rectangular lawn is 160 * 120 = 19,200 square feet.
To cover this area, we need 19,200 / 200 = 96 bags of fertilizer.
Therefore, the answer is choice B, 10 bags (rounded up from 9.6).

Quiz 5: Ratio, Proportion, and Percent

For the proportion, find the unknown number n. - $\frac { \mathrm { n } } { \frac { 11 } { 13 } } = \frac { 2 \frac { 1 } { 6 } } { 1 \frac { 1 } { 10 } }$

Solve. -One pound of a product yieldsds $2 \frac { 1 } { 4 }$ cups. How many pounds of this product will be required by a recipe that calls for 6 cups of the product?

Solve. -There are 0.5 milligrams of iron in a 3.5 ounce serving of cod. How much iron is in 4 ounces of cod? Round the answer to one decimal place.

Solve. -The ratio of a quarterback's completed passes to attempted passes is 7 to 8. If he attempted 16 passes, find how many passes he completed. Round to the nearest whole number if necessary.

Solve. -On an architect's blueprint, 1 inch corresponds to 8 feet. Find the length of a wall represented by a lineine $5 \frac { 1 } { 4 }$ inches long on the blueprint. Round to the nearest tenth if necessary.

For the proportion, find the unknown number n. - $\frac { \mathrm { n } } { 10 } = \frac { 1 } { 2 \frac { 1 } { 2 } }$

For the proportion, find the unknown number n. - $\frac { 3 } { \frac { 1 } { 6 } } = \frac { 18 } { n }$

Solve. -The scale on a map states that 1 centimeter corresponds to 30 kilometers. On the map, two cities are 0.7 cm apart. Find the actual distance.

For the proportion, find the unknown number n. - $\frac { \frac { 1 } { 3 } } { \frac { 3 } { 9 } } = \frac { 17 } { n }$

Solve. -On an architect's blueprint, 1 inch corresponds to 4 feet. If an exterior wall is 24 feet long, find how long the blueprint measurement should be. Write answer as a mixed number if necessary.

Solve. -The ratio of a basketball player's completed free throws to attempted free throws is 5 to 6. If she completed 20 free throws, find how many free throws she attempted. Round to the nearest whole number if necessary.

Solve. -It takes Winnie 22 minutes to word process and spell check 10 pages. Find how long it takes her to word process and spell check 45 pages. Round answers to the nearest whole number if necessary.

For the proportion, find the unknown number n. - $\frac { 0.6 } { 4.2 } = \frac { 5 } { n }$

Solve. -A baseball player makes 4 hits in every 7 times at bat. At this rate, if he made 24 hits, find how many times he batted.

Solve. -A punch recipe calls for mixing 6 parts of grape juice with 7 parts of lemon juice. Find how much grape juice should be mixed with 126 ounces of lemon juice.

For the proportion, find the unknown number n. - $\frac { 8.4 } { 14 } = \frac { n } { 2.8 }$

Solve. -A can of lemonade comes with a measuring scoop and directions for mixing are 8 scoops of mix for every 24 cups of water. How much water is needed to make the entire can of lemonade if there are 40 scoops of mix?

For the proportion, find the unknown number n. - $\frac { 294 } { 62 } = \frac { n } { 558 }$

Solve. -It takes Frank 10 minutes to word process and spell check 6 pages. Find how many pages he can word process and spell check in 0.5 hours. Round answers to the nearest tenth if necessary.

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 160 feet by 120 feet.

Quiz 5: Ratio, Proportion, and Percent

For the proportion, find the unknown number n. - n1113=2161110\frac { \mathrm { n } } { \frac { 11 } { 13 } } = \frac { 2 \frac { 1 } { 6 } } { 1 \frac { 1 } { 10 } }1311​n​=1101​261​​

Solve. -One pound of a product yieldsds 2142 \frac { 1 } { 4 }241​ cups. How many pounds of this product will be required by a recipe that calls for 6 cups of the product?

Solve. -There are 0.5 milligrams of iron in a 3.5 ounce serving of cod. How much iron is in 4 ounces of cod? Round the answer to one decimal place.

Solve. -The ratio of a quarterback's completed passes to attempted passes is 7 to 8. If he attempted 16 passes, find how many passes he completed. Round to the nearest whole number if necessary.

Solve. -On an architect's blueprint, 1 inch corresponds to 8 feet. Find the length of a wall represented by a lineine 5145 \frac { 1 } { 4 }541​ inches long on the blueprint. Round to the nearest tenth if necessary.

For the proportion, find the unknown number n. - n10=1212\frac { \mathrm { n } } { 10 } = \frac { 1 } { 2 \frac { 1 } { 2 } }10n​=221​1​

For the proportion, find the unknown number n. - 316=18n\frac { 3 } { \frac { 1 } { 6 } } = \frac { 18 } { n }61​3​=n18​

Solve. -The scale on a map states that 1 centimeter corresponds to 30 kilometers. On the map, two cities are 0.7 cm apart. Find the actual distance.

For the proportion, find the unknown number n. - 1339=17n\frac { \frac { 1 } { 3 } } { \frac { 3 } { 9 } } = \frac { 17 } { n }93​31​​=n17​

Solve. -On an architect's blueprint, 1 inch corresponds to 4 feet. If an exterior wall is 24 feet long, find how long the blueprint measurement should be. Write answer as a mixed number if necessary.

Solve. -The ratio of a basketball player's completed free throws to attempted free throws is 5 to 6. If she completed 20 free throws, find how many free throws she attempted. Round to the nearest whole number if necessary.

Solve. -It takes Winnie 22 minutes to word process and spell check 10 pages. Find how long it takes her to word process and spell check 45 pages. Round answers to the nearest whole number if necessary.

For the proportion, find the unknown number n. - 0.64.2=5n\frac { 0.6 } { 4.2 } = \frac { 5 } { n }4.20.6​=n5​

Solve. -A baseball player makes 4 hits in every 7 times at bat. At this rate, if he made 24 hits, find how many times he batted.

Solve. -A punch recipe calls for mixing 6 parts of grape juice with 7 parts of lemon juice. Find how much grape juice should be mixed with 126 ounces of lemon juice.

For the proportion, find the unknown number n. - 8.414=n2.8\frac { 8.4 } { 14 } = \frac { n } { 2.8 }148.4​=2.8n​

Solve. -A can of lemonade comes with a measuring scoop and directions for mixing are 8 scoops of mix for every 24 cups of water. How much water is needed to make the entire can of lemonade if there are 40 scoops of mix?

For the proportion, find the unknown number n. - 29462=n558\frac { 294 } { 62 } = \frac { n } { 558 }62294​=558n​

Solve. -It takes Frank 10 minutes to word process and spell check 6 pages. Find how many pages he can word process and spell check in 0.5 hours. Round answers to the nearest tenth if necessary.

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 160 feet by 120 feet.

For the proportion, find the unknown number n. - $\frac { \mathrm { n } } { \frac { 11 } { 13 } } = \frac { 2 \frac { 1 } { 6 } } { 1 \frac { 1 } { 10 } }$

Solve. -One pound of a product yieldsds $2 \frac { 1 } { 4 }$ cups. How many pounds of this product will be required by a recipe that calls for 6 cups of the product?

Solve. -On an architect's blueprint, 1 inch corresponds to 8 feet. Find the length of a wall represented by a lineine $5 \frac { 1 } { 4 }$ inches long on the blueprint. Round to the nearest tenth if necessary.

For the proportion, find the unknown number n. - $\frac { \mathrm { n } } { 10 } = \frac { 1 } { 2 \frac { 1 } { 2 } }$

For the proportion, find the unknown number n. - $\frac { 3 } { \frac { 1 } { 6 } } = \frac { 18 } { n }$

For the proportion, find the unknown number n. - $\frac { \frac { 1 } { 3 } } { \frac { 3 } { 9 } } = \frac { 17 } { n }$

For the proportion, find the unknown number n. - $\frac { 0.6 } { 4.2 } = \frac { 5 } { n }$

For the proportion, find the unknown number n. - $\frac { 8.4 } { 14 } = \frac { n } { 2.8 }$

For the proportion, find the unknown number n. - $\frac { 294 } { 62 } = \frac { n } { 558 }$