Question 1

Solve the equation.
-3x + 23 = 2x + 100

Accepted Answer

To solve the equation 3x + 23 = 2x + 100, subtract 2x from both sides to get x + 23 = 100. Then, subtract 23 from both sides to find x = 77.

Question 2

Solve the equation.
-2x + 8 = x + 36

Accepted Answer

The answer of Solve the equation.
-2x + 8 = x...

Question 3

Solve the equation.
-21 - x = 3x + 5

Accepted Answer

The answer of Solve the equation.
-21 - x = 3x...

Question 4

Solve the equation.
-2x + 7 = 2(x + 7)

Accepted Answer

The equation simplifies to 2x + 7 = 2x + 14. Subtracting 2x from both sides gives 7 = 14, which is a contradiction, indicating there is no solution.

Question 5

Write an equation relating the variables in the situation described.
-The amount of money M in a piggy bank containing only nickels and dimes d, when there are five more nickels than dimes.

Accepted Answer

The answer of Write an equation relating the variables in...

Question 6

Write an equation relating the variables in the situation described.
-Your pay P for h hours if you are paid $9 for the first two hours and $32 for each additional hour and you work for more than two hours.

Accepted Answer

If you work for more than two hours, you get paid $9 for the first two hours and $32 for each additional hour. So, the total pay P for h hours is:P = 9 + 32 ( h - 2 )

Question 7

Write an equation relating the variables in the situation described.
-The cost C of renting a video movie for n days if the charge is $2 plus $3 per day of renting.

Accepted Answer

The cost C consists of a fixed charge of $2 plus an additional charge of $3 per day for n days, which is represented by the equation $C = 2 + 3n$.

Question 8

Write an equation relating the variables in the situation described.
-The sum S of three consecutive integers if the middle number is x.

Accepted Answer

The three consecutive integers can be represented as (x-1), x, and (x+1). Their sum, S, is (x-1) + x + (x+1) = 3x.

Question 9

Write an equation relating the variables in the situation described.
-The cost C of renting a video movie for n days if the charge is $3 deposit plus $2 per day of renting. The deposit is returned when the movie is returned.

Accepted Answer

The answer of Write an equation relating the variables in...

Question 10

Write an equation relating the variables in the situation described.
-The cost C in dollars of having an electrician come to your house to do a repair job in h hours if he charges $22 for coming to the house and $30 for each hour.

Accepted Answer

The total cost C consists of a fixed charge of $22 plus $30 for each hour of work, which is represented by the equation C = 22 + 30h.

Question 11

Write an expression in terms of the given variable(s)that represents the indicated quantity.
-Mark has half as many stickers as Derek. If Derek has d stickers and Mark m stickers, and Derek gives Mark 10 stickers, how many stickers does each have in terms of d?

Accepted Answer

Initially, Mark has $m = \frac{d}{2}$ stickers. After Derek gives Mark 10 stickers, Derek will have $d - 10$ stickers, and Mark will have $\frac{d}{2} + 10$ stickers.

Question 12

Solve the equation.
-x - 3 = 36

Accepted Answer

The answer of Solve the equation.
-x - 3 = 36
...

Question 13

Solve the problem.
-Consider the following $1 \times 1,2 \times 2$, and $3 \times 3$ matchstick designs.

How many matchsticks are needed for a $12 \times 12$ design?

Accepted Answer

The answer of Solve the problem.
-Consider the following \(1 \times...

Question 14

Write an equation relating the variables in the situation described.
-The temperature in Fahrenheit F if five times the temperature in Fahrenheit is equal to the sum of nine times the temperature in degree Celsius C and 160.

Accepted Answer

The correct equation for converting Celsius to Fahrenheit is $F = \frac{9}{5}C + 32$, which matches the given situation when simplified.

Question 15

Write an equation relating the variables in the situation described.
-The number of words W typed in t minutes if you type 29 words in one minute.

Accepted Answer

The number of words typed in t minutes is the product of the number of words typed per minute (29) and the number of minutes (t), hence $W = 29t$.

Question 16

Solve the equation.
-7(3x - 12)= 6(3x - 12)

Accepted Answer

The answer of Solve the equation.
-7(3x - 12)= 6(3x -...

Question 17

Solve the equation.
-7(2x + 1)+ 9(2x + 1)= 144

Accepted Answer

The answer of Solve the equation.
-7(2x + 1)+ 9(2x +...

Question 18

Write an equation relating the variables in the situation described.
-The distance D traveled in T hours at a constant speed of S mph.

Accepted Answer

The correct equation that relates distance (D), time (T), and speed (S) is $D = ST$, which states that distance equals speed times time.

Question 19

Write an equation relating the variables in the situation described.
-The sum S of three integers when the largest number is five times the smallest m and two more than the middle one.

Accepted Answer

The largest integer is $5m$, the middle integer is $5m - 2$, and the smallest integer is $m$. The sum $S$ is $m + (5m - 2) + 5m = 11m - 2$.

Question 20

Solve the problem.
-The sum of three consecutive integers is 519. Find the numbers.

Accepted Answer

The answer of Solve the problem.
-The sum of three consecutive...

Quiz 8: Real Numbers and Algebraic Thinking

Solve the equation. -3x + 23 = 2x + 100

Solve the equation. -2x + 8 = x + 36

Solve the equation. -21 - x = 3x + 5

Solve the equation. -2x + 7 = 2(x + 7)

Write an equation relating the variables in the situation described. -The amount of money M in a piggy bank containing only nickels and dimes d, when there are five more nickels than dimes.

Write an equation relating the variables in the situation described. -Your pay P for h hours if you are paid $9 for the first two hours and $32 for each additional hour and you work for more than two hours.

Write an equation relating the variables in the situation described. -The cost C of renting a video movie for n days if the charge is $2 plus $3 per day of renting.

Write an equation relating the variables in the situation described. -The sum S of three consecutive integers if the middle number is x.

Write an equation relating the variables in the situation described. -The cost C of renting a video movie for n days if the charge is $3 deposit plus $2 per day of renting. The deposit is returned when the movie is returned.

Write an equation relating the variables in the situation described. -The cost C in dollars of having an electrician come to your house to do a repair job in h hours if he charges $22 for coming to the house and $30 for each hour.

Write an expression in terms of the given variable(s) that represents the indicated quantity. -Mark has half as many stickers as Derek. If Derek has d stickers and Mark m stickers, and Derek gives Mark 10 stickers, how many stickers does each have in terms of d?

Solve the equation. -x - 3 = 36

Write an equation relating the variables in the situation described. -The temperature in Fahrenheit F if five times the temperature in Fahrenheit is equal to the sum of nine times the temperature in degree Celsius C and 160.

Write an equation relating the variables in the situation described. -The number of words W typed in t minutes if you type 29 words in one minute.

Solve the equation. -7(3x - 12) = 6(3x - 12)

Solve the equation. -7(2x + 1) + 9(2x + 1) = 144

Write an equation relating the variables in the situation described. -The distance D traveled in T hours at a constant speed of S mph.

Write an equation relating the variables in the situation described. -The sum S of three integers when the largest number is five times the smallest m and two more than the middle one.

Solve the problem. -The sum of three consecutive integers is 519. Find the numbers.