Question

writing equations
independent practice
name ______
date ____ pd
in 1-2, write an equation to represent the situation. then, solve the equation.

1. eddie ordered customized cups. he was charged a $30 design fee plus $8 per cup. his total order was $334. how many cups did eddie order?

a. equation: ______
b. solution: ______

1. damian is monitoring the temperature of the swimming pool. it is currently 86.8° and cooling 0.5° per minute. after how many minutes will the swimming pool be 80.8°?

a. equation: ______
b. solution: ______

1. create and write a real - world situation that could be represented by the equation below:

$5x + 15 = 45$
_____________________________________
_____________________________________
_____________________________________

1. determine if the statements below correctly describe the equation, $20 + 12x = 240$.

______ a. joanie earns $12 per hour, plus a $20 bonus for completing the training program. this week joanie earned $240.
______ b. isaiah is saving $12 per week from his allowance. after 20 weeks, isaiah has $240.
______ c. felix exercises by spending 12 minutes warming up and then running for 20 minutes. he has exercised a total of 240 minutes this month.

1. zoe and claire are sisters. they are giving clues about their heights. write an equation and solve to determine the height of both zoe and claire.

#1: claire is twice as tall as zoe.
#2: together, claire and zoe are 108 inches tall.

Explanation:

Problem 1: Eddie's Cups

a. Equation:

Let \( x \) be the number of cups. The total cost is the design fee plus the cost per cup times the number of cups. So the equation is \( 30 + 8x = 334 \).

b. Solution:

Step1: Subtract 30 from both sides

\( 30 + 8x - 30 = 334 - 30 \)
\( 8x = 304 \)

Step2: Divide both sides by 8

\( \frac{8x}{8} = \frac{304}{8} \)
\( x = 38 \)

Problem 2: Pool Temperature

a. Equation:

Let \( t \) be the number of minutes. The final temperature is the initial temperature minus the cooling rate times the number of minutes. So the equation is \( 86.8 - 0.5t = 80.8 \).

b. Solution:

Step1: Subtract 86.8 from both sides

\( 86.8 - 0.5t - 86.8 = 80.8 - 86.8 \)
\( -0.5t = -6 \)

Step2: Divide both sides by -0.5

\( \frac{-0.5t}{-0.5} = \frac{-6}{-0.5} \)
\( t = 12 \)

Problem 3: Real - World Situation for \( 5x + 15 = 45 \)

A possible situation: A movie rental service charges a $15 monthly fee plus $5 per movie rented. If your total bill for the month is $45, how many movies (\( x \)) did you rent?

Problem 4: Analyzing \( 20 + 12x = 240 \)

a.

Joanie's earnings: $20 bonus (constant) plus $12 per hour (\( x \) hours) equals $240. This matches the equation \( 20+12x = 240 \). So this statement is correct (mark with a check or "Yes").

b.

Isaiah's savings: If he saves $12 per week for 20 weeks, the equation should be \( 12\times20=240 \), not \( 20 + 12x = 240 \). So this statement is incorrect (mark with an "X" or "No").

c.

Felix's exercise: 12 minutes warming up and 20 minutes running per session. The equation for total minutes would be different from \( 20 + 12x = 240 \). So this statement is incorrect (mark with an "X" or "No").

Problem 5: Zoe and Claire's Heights

Let \( z \) be Zoe's height (in inches). Then Claire's height is \( 2z \) (since Claire is twice as tall as Zoe). The sum of their heights is 108 inches.

Equation:

\( z + 2z=108 \) (or \( 3z = 108 \))

Solution:

Step1: Combine like terms

\( 3z=108 \)

Step2: Divide both sides by 3

\( \frac{3z}{3}=\frac{108}{3} \)
\( z = 36 \)

Claire's height is \( 2z=2\times36 = 72 \) inches.

Answer:

s:

1. a. \( 30 + 8x = 334 \); b. \( 38 \) cups
2. a. \( 86.8 - 0.5t = 80.8 \); b. \( 12 \) minutes
3. (Example) A movie rental service charges a $15 monthly fee plus $5 per movie rented. If your total bill for the month is $45, how many movies (\( x \)) did you rent?
4. a. Correct; b. Incorrect; c. Incorrect
5. Equation: \( z + 2z = 108 \) (or \( 3z = 108 \)); Zoe's height: 36 inches, Claire's height: 72 inches