Question

chapter 1 test : solving linear equations & stats
(show your work to receive full credit!)
statistics

1. looking at the list of numbers, find the mean, median, mode, range and standard deviation of that list of numbers.

project scores
{10, 100, 25, 35, 98, 12, 98, 88, 99}
mean
62.7
mode
98
range
90
median
88
solving simple equations

1. a) solve for x: x - 9 = 16

x = 25
b) solve for g: 8g = -64
solving multi-step equations

1. a) solve for y: 2y + 4 = 60

b) solve for x: \frac{x - 8}{5}=10

1. charlene has a lemonade stand. she spent $31 building the stand and buying the supplies. she made $350 in one day, after selling cups of lemonade for $3.00. what equation represents the profit for the day? how many cups of lemonade did she sell?

Explanation:

Step1: Solve for \( y \) in \( 2y + 4 = 60 \)

Subtract 4 from both sides:
\( 2y+4 - 4=60 - 4 \)
\( 2y = 56 \)
Divide both sides by 2:
\( y=\frac{56}{2}=28 \)

Step2: Solve for \( x \) in \( \frac{x - 8}{5}=10 \)

Multiply both sides by 5:
\( \frac{x - 8}{5}\times5=10\times5 \)
\( x - 8 = 50 \)
Add 8 to both sides:
\( x=50 + 8=58 \)

Step3: Set up the profit equation

Let \( x \) be the number of cups sold.
Revenue is \( 3x \), cost is \( 31 \), profit is \( 350 \).
The profit equation is \( 3x-31 = 350 \)
Add 31 to both sides:
\( 3x-31+31 = 350+31 \)
\( 3x=381 \)
Divide both sides by 3:
\( x=\frac{381}{3}=127 \)

Answer:

1. For \( 2y + 4 = 60 \), \( y = 28 \)
2. For \( \frac{x - 8}{5}=10 \), \( x = 58 \)
3. The profit equation is \( 3x-31 = 350 \), and the number of cups sold \( x = 127 \)