Question

in exercises 1–6, solve the equation. check your solution.

1. $9 + k = 12$
2. $14 = 9 + p$
3. $\frac{h}{2} = 7 + 10$
4. $\frac{k - 4}{3} = 1$
5. $15 = 2b + 5b$
6. $81 + 4 = 71 + 8$

1. the cost $c$ (in dollars) of renting a paddleboat for $h$ hours is given by $c = 25 + 7h$. after how many hours is the cost $\\$81$?

in exercises 8–10, solve the equation. check your solution.

1. $-3(2r + 7) = 3$
2. $4 + 6(1 - m) = 4$
3. $19 = 15a - 4(3a - 1)$

in exercises 11 and 12, find the value of the variable. then find the angle measures of the polygon. use a protractor to check the reasonableness of your answer.

1. sum of angle measures: $180^\circ$

(triangle with angles $n^\circ$, $6n^\circ$, $60^\circ$)

1. sum of angle measures: $360^\circ$

(quadrilateral with angles $7x^\circ$, $15x^\circ$, $12x^\circ$, $7x^\circ$)

in exercises 13–16, write and solve an equation to find the number.

1. the sum of 4 and three times a number is 19.
2. the difference of twice a number and 7 is 9.
3. ten less the quotient of a number and 3 is 6.
4. five times the sum of a number and 4 is $-15$.

in exercises 17 and 18, write and solve an equation to answer the question. check that the units on each side of the equation balance.

1. you purchase two bottles of sunscreen and a hat. the hat costs $\\$6.50$. you pay 6% sales tax. you pay a total of $\\$16.43$. how much does one bottle of sunscreen cost?
2. the perimeter of a patio is 64 feet. the width of the patio is 12 feet and the length of the patio is $(x + 6)$ feet. what is the length of the patio?

Explanation:

Let's solve exercise 13 as an example.

Step 1: Define the variable

Let the number be \( x \).

Step 2: Translate the problem into an equation

The sum of 4 and three times a number is 19. So, \( 4 + 3x = 19 \).

Step 3: Solve for \( x \)

Subtract 4 from both sides: \( 3x = 19 - 4 \)
\( 3x = 15 \)
Divide both sides by 3: \( x = \frac{15}{3} \)
\( x = 5 \)

Answer:

The number is 5.