Question 1

Jill is 12 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at $1.5 \mathrm{~km} / \mathrm{hr}$. They meet in 3 hours. How fast is Joe walking?

Accepted Answer

In 3 hours, Jill walks $3 \times 1.5 = 4.5$ kilometers. Since they meet after 3 hours, the total distance covered by both is 12 kilometers. Thus, Joe covers $12 - 4.5 = 7.5$ kilometers in 3 hours, walking at a speed of $7.5 / 3 = 2.5$ kilometers/hour.

Question 2

From a point on a straight road, two cars are driven in opposite directions, one at 22 miles per hour and the other at 62 miles per hour. In how many hours will they be 420 miles apart?

Accepted Answer

Since the cars are moving in opposite directions, their speeds add up. So, their relative speed is 22 + 62 = 84 miles per hour. To find the time, divide the total distance by the relative speed: 420 miles / 84 miles per hour = 5 hours.

Question 3

From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 10 miles per hour and Fred rides 14 miles per hour. In how many hours will they be 120 miles apart?

Accepted Answer

Since John and Fred are moving in opposite directions, their speeds add up. Together, they cover 10 + 14 = 24 miles per hour. To be 120 miles apart, it will take 120 / 24 = 5 hours.

Question 4

From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 13 miles per hour. In how many hours will they be 46 miles apart?

Accepted Answer

The answer of From a point on a river, two...

Question 5

A car traveling 68 miles per hour passes a bus traveling 61 in the same direction on the highway. If they maintain their speeds, how long will it take them to be 17.5 miles apart?

Accepted Answer

To find the time it takes for the car and bus to be 17.5 miles apart, we calculate the relative speed between them. The car travels at 68 mph and the bus at 61 mph, so their relative speed is 68 - 61 = 7 mph. To cover a distance of 17.5 miles at a speed of 7 mph, it takes 17.5 / 7 = 2.5 hours.

Question 6

On her way to a holiday weekend, Nancy drove $2 \frac{1}{2}$ hours in rush- hour traffic. When traffic eased up, she was able to increase her speed by 42 miles per hour and drove another $4 \frac{1}{2}$ hours. If the entire trip was 371 miles, how fast did she drive in rush- hour traffic?

Accepted Answer

The answer of On her way to a holiday weekend,...

Question 7

Andy has some $\$ 10$ bills and some $\$ 20$ bills in a shoebox under his bed. He has a total of 42 bills worth a total of $\$ 550$. How many $\$ 20$ bills does he have?

Accepted Answer

The answer of Andy has some $\$ 10$ bills and...

Question 8

There are two types of tickets for a school play: child tickets that sell for $\$ 3$ each and adult tickets that sell for $\$ 6$ each. A total of 112 tickets are sold, bringing in a total of $\$ 561$. How many adult tickets are sold?

Accepted Answer

The answer of There are two types of tickets for...

Question 9

There are two types of tickets for a school play: student tickets and tickets for the general public. The total cost for one student ticket and one general public ticket is $\$ 8$. The total cost for 8 student tickets and 14 general public tickets is $\$ 100$. How much does a general public ticket cost?

Accepted Answer

The answer of There are two types of tickets for...

Question 10

There are two types of tickets for a school play: student tickets and tickets for the general public. The total cost for one student ticket and one general public ticket is $\$ 10$. The total cost for 10 student tickets and 12 general public tickets is $\$ 116$. How much does a student ticket cost?

Accepted Answer

Let the cost of a student ticket be $x$ dollars and the cost of a general public ticket be $y$ dollars. From the given information, we have two equations:1. $x + y = 10$2. $10x + 12y = 116$Solving these equations simultaneously, we can find the value of $x$. Multiplying the first equation by 10 gives $10x + 10y = 100$. Subtracting this from the second equation gives $2y = 16$, so $y = 8$. Substituting $y = 8$ into the first equation gives $x + 8 = 10$, so $x = 2$. Therefore, a student ticket costs \$2.

Question 11

Matthew has two different stocks. One of the stocks is worth $\$ 7$ more per share than the other. He has 13 shares of the more valuable stock and 31 shares of the other stock. His total assets in stocks is $\$ 1235$. How much is the more expensive stock worth per share?

Accepted Answer

Let the price of the less expensive stock be $x$ dollars per share. Then, the price of the more expensive stock is $x + 7$ dollars per share. The total value of the stocks is given by $13(x + 7) + 31x = 1235$. Simplifying, we get $44x + 91 = 1235$, leading to $44x = 1144$, and $x = 26$. Therefore, the more expensive stock is worth $26 + 7 = \$33$ per share.

Question 12

Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 15 shares of the more valuable stock and 33 shares of the other stock. His total assets in stocks is $\$ 1890$. How much is the more expensive stock worth per share?

Accepted Answer

Let the price of the less expensive stock be $x$ per share. Therefore, the more expensive stock is worth $2x$ per share. The total value of the stocks is given by $15(2x) + 33(x) = 1890$. Simplifying, we get $30x + 33x = 1890$, which simplifies to $63x = 1890$. Solving for $x$, we find $x = 30$, making the more expensive stock $2x = 60$ per share.

Question 13

Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 13 shares of the more valuable stock and 45 shares of the other stock. His total assets in stocks is $\$ 2272$. How much is the less expensive stock worth per share?

Accepted Answer

Let the price of the less expensive stock be $ x $. Then the price of the more expensive stock is $ 2x $. The total value of the stocks is $ 13(2x) + 45(x) = 2272 $. Solving $ 26x + 45x = 2272 $ gives $ 71x = 2272 $, so $ x = 32 $.

Question 14

$\frac{n}{34}=\frac{9}{17}$

Accepted Answer

The answer of $\frac{n}{34}=\frac{9}{17}$

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Question 15

$\frac{1}{2}=\frac{n}{17}$

Accepted Answer

The answer of $\frac{1}{2}=\frac{n}{17}$

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Question 16

$\frac{47}{188}=\frac{9}{n}$

Accepted Answer

To solve for $n$ in the equation $\frac{47}{188}=\frac{9}{n}$, simplify the fraction on the left side. $\frac{47}{188}$ simplifies to $\frac{1}{4}$ because $47$ and $188$ are both divisible by $47$. Then, set the simplified fraction equal to the fraction on the right side: $\frac{1}{4}=\frac{9}{n}$. Cross-multiply to solve for $n$: $1 \cdot n = 4 \cdot 9$, which simplifies to $n = 36$.

Question 17

$\frac{4}{n}=\frac{8}{4}$

Accepted Answer

The answer of $\frac{4}{n}=\frac{8}{4}$

...

Question 18

$\frac{4 n-2}{9}=\frac{n}{5}$

Accepted Answer

The answer of $\frac{4 n-2}{9}=\frac{n}{5}$

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Question 19

$\frac{3}{2}=\frac{n+5}{8}$

Accepted Answer

To solve for $n$, cross-multiply to get $3 \times 8 = 2(n + 5)$. Simplifying, $24 = 2n + 10$, then $14 = 2n$, so $n = 7$.

Question 20

$\frac{n+8}{12}=\frac{10}{7}$

Accepted Answer

The answer of $\frac{n+8}{12}=\frac{10}{7}$

...

Quiz 2: Linear and Absolute Value Equations and Inequalities

Jill is 12 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at $1.5 \mathrm{~km} / \mathrm{hr}$ . They meet in 3 hours. How fast is Joe walking?

From a point on a straight road, two cars are driven in opposite directions, one at 22 miles per hour and the other at 62 miles per hour. In how many hours will they be 420 miles apart?

From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 10 miles per hour and Fred rides 14 miles per hour. In how many hours will they be 120 miles apart?

From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 13 miles per hour. In how many hours will they be 46 miles apart?

A car traveling 68 miles per hour passes a bus traveling 61 in the same direction on the highway. If they maintain their speeds, how long will it take them to be 17.5 miles apart?

On her way to a holiday weekend, Nancy drove $2 \frac{1}{2}$ hours in rush- hour traffic. When traffic eased up, she was able to increase her speed by 42 miles per hour and drove another $4 \frac{1}{2}$ hours. If the entire trip was 371 miles, how fast did she drive in rush- hour traffic?

Andy has some $\$ 10$ bills and some $\$ 20$ bills in a shoebox under his bed. He has a total of 42 bills worth a total of $\$ 550$ . How many $\$ 20$ bills does he have?

There are two types of tickets for a school play: child tickets that sell for $\$ 3$ each and adult tickets that sell for $\$ 6$ each. A total of 112 tickets are sold, bringing in a total of $\$ 561$ . How many adult tickets are sold?

Matthew has two different stocks. One of the stocks is worth $\$ 7$ more per share than the other. He has 13 shares of the more valuable stock and 31 shares of the other stock. His total assets in stocks is $\$ 1235$ . How much is the more expensive stock worth per share?

Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 15 shares of the more valuable stock and 33 shares of the other stock. His total assets in stocks is $\$ 1890$ . How much is the more expensive stock worth per share?

Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 13 shares of the more valuable stock and 45 shares of the other stock. His total assets in stocks is $\$ 2272$ . How much is the less expensive stock worth per share?

$\frac{n}{34}=\frac{9}{17}$

$\frac{1}{2}=\frac{n}{17}$

$\frac{47}{188}=\frac{9}{n}$

$\frac{4}{n}=\frac{8}{4}$

$\frac{4 n-2}{9}=\frac{n}{5}$

$\frac{3}{2}=\frac{n+5}{8}$

$\frac{n+8}{12}=\frac{10}{7}$

Quiz 2: Linear and Absolute Value Equations and Inequalities

Jill is 12 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 1.5 km/hr1.5 \mathrm{~km} / \mathrm{hr}1.5 km/hr . They meet in 3 hours. How fast is Joe walking?

From a point on a straight road, two cars are driven in opposite directions, one at 22 miles per hour and the other at 62 miles per hour. In how many hours will they be 420 miles apart?

From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 10 miles per hour and Fred rides 14 miles per hour. In how many hours will they be 120 miles apart?

From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 13 miles per hour. In how many hours will they be 46 miles apart?

A car traveling 68 miles per hour passes a bus traveling 61 in the same direction on the highway. If they maintain their speeds, how long will it take them to be 17.5 miles apart?

Andy has some $10\$ 10$10 bills and some $20\$ 20$20 bills in a shoebox under his bed. He has a total of 42 bills worth a total of $550\$ 550$550 . How many $20\$ 20$20 bills does he have?

There are two types of tickets for a school play: child tickets that sell for $3\$ 3$3 each and adult tickets that sell for $6\$ 6$6 each. A total of 112 tickets are sold, bringing in a total of $561\$ 561$561 . How many adult tickets are sold?

Matthew has two different stocks. One of the stocks is worth $7\$ 7$7 more per share than the other. He has 13 shares of the more valuable stock and 31 shares of the other stock. His total assets in stocks is $1235\$ 1235$1235 . How much is the more expensive stock worth per share?

Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 15 shares of the more valuable stock and 33 shares of the other stock. His total assets in stocks is $1890\$ 1890$1890 . How much is the more expensive stock worth per share?

Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 13 shares of the more valuable stock and 45 shares of the other stock. His total assets in stocks is $2272\$ 2272$2272 . How much is the less expensive stock worth per share?

n34=917\frac{n}{34}=\frac{9}{17}34n​=179​

12=n17\frac{1}{2}=\frac{n}{17}21​=17n​

47188=9n\frac{47}{188}=\frac{9}{n}18847​=n9​

4n=84\frac{4}{n}=\frac{8}{4}n4​=48​

4n−29=n5\frac{4 n-2}{9}=\frac{n}{5}94n−2​=5n​

32=n+58\frac{3}{2}=\frac{n+5}{8}23​=8n+5​

n+812=107\frac{n+8}{12}=\frac{10}{7}12n+8​=710​

Jill is 12 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at $1.5 \mathrm{~km} / \mathrm{hr}$ . They meet in 3 hours. How fast is Joe walking?

Andy has some $\$ 10$ bills and some $\$ 20$ bills in a shoebox under his bed. He has a total of 42 bills worth a total of $\$ 550$ . How many $\$ 20$ bills does he have?

There are two types of tickets for a school play: child tickets that sell for $\$ 3$ each and adult tickets that sell for $\$ 6$ each. A total of 112 tickets are sold, bringing in a total of $\$ 561$ . How many adult tickets are sold?

Matthew has two different stocks. One of the stocks is worth $\$ 7$ more per share than the other. He has 13 shares of the more valuable stock and 31 shares of the other stock. His total assets in stocks is $\$ 1235$ . How much is the more expensive stock worth per share?

Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 15 shares of the more valuable stock and 33 shares of the other stock. His total assets in stocks is $\$ 1890$ . How much is the more expensive stock worth per share?

Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 13 shares of the more valuable stock and 45 shares of the other stock. His total assets in stocks is $\$ 2272$ . How much is the less expensive stock worth per share?

$\frac{n}{34}=\frac{9}{17}$

$\frac{1}{2}=\frac{n}{17}$

$\frac{47}{188}=\frac{9}{n}$

$\frac{4}{n}=\frac{8}{4}$

$\frac{4 n-2}{9}=\frac{n}{5}$

$\frac{3}{2}=\frac{n+5}{8}$

$\frac{n+8}{12}=\frac{10}{7}$