Algebra 1-3

What value of $ x $ is the solution of the equation $\frac{6x - 10}{2} = x + 1$? Enter your answer in the space provided.

Terry has $125 in their checking account. At the end of each month, they will add $50 to the account. Which equation describes the total amount $ C $, in dollars, that Terry will have in their account at the end of month $ m $? Select one answer.

• C = 75m

• C = 175m

• C = 50 + 125m

• C = 125 + 50m

The formula for the volume of a pyramid is $ V = \frac{1}{3} Bh $. What is $ h $ expressed in terms of $ B $ and $ V $? Select one answer.

• $ h = \frac{1}{3} VB $

• $ h = \frac{3V}{B} $

• $ h = \frac{V}{3B} $

• $ h = 3VB $

The average price of a movie ticket in the United States from 2000 to 2020 is modeled by the expression $ 5.43 + 0.20x $, where $ x $ represents the number of years since 2000. Identify the part(s) of the expression that corresponds to the cost of movie tickets in 2000.

• $ 0.20 $

• $ 0.20x $

• $ 5.43 $

• $ 5.43 + 0.20x $

Graph the system of inequalities in the $xy$-plane. \[\begin{cases} y < \frac{1}{2}x - 1 \\ y \leq -3x + 2 \end{cases}\]

• A

• B

• C

• D

A system of equations is given. \[\begin{align*}y &= 7x - 1 \\y &= 3x + 2 \end{align*}\] What is the value of \( x \) in the solution \( (x, y) \) to the system?

• \(\frac{3}{4}\)

• \(\frac{3}{10}\)

• \(\frac{1}{4}\)

• \(\frac{1}{10}\)

Lance decided they wanted to go to the neighborhood carnival during Spring Break. The carnival charges a one-time entry fee of $12.50 and $2.50 per ride. Define a variable and write an expression that represents the scenario.

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If Lance saved $50 to attend the carnival, how many rides can he ride? Show your work or explain how you found your answer.

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Rose will purchase hats and scarves for the students in her class this year. - She can spend at most $165 on hats and scarves. - Hats cost $3 each, and scarves cost $5 each. - She must buy at most two times as many hats as scarves. Write a system of inequalities that can determine the number of hats and scarves Rose can buy. Select one answer.

• 3x + 5y ≤ 165 and 2x ≤ y

• 3x + 5y ≥ 165 and 2x ≥ y

• 3x + 5y ≤ 165 and x ≤ 2y

• 3x + 5y ≥ 165 and x ≥ 2y

A student earns money during the summer by charging $25 per hour tutoring neighborhood kids and $35 per hour cutting their neighbor's grass. The student cannot work more than 35 hours per week. The student wants to earn at least $475 each week. Let x represent the number of hours tutoring kids in the neighborhood and y represent the number of hours spent cutting grass his neighbor’s grass. Select the two equations below that can be used to create a system of inequalities that represents the given constraints.

• 25x + 35y ≤ 35

• x + y ≤ 35

• 25x + 35y ≥ 475

• 35x + 25y ≤ 35

• 35x + 25y ≥ 475