ACT 1 Alg: Write linear equations and inequalities

Welcome to your ACT 1 Alg: Write linear equations and inequalities

$Q_{1}:$ Maya enters a highway at mile marker $299$ and travels south from Ft. Wayne toward Indianapolis, driving at an average speed of $50$ miles per hour. She wants to rendezvous with Kiyomi, who is entering the same highway at mile marker $203$ and driving north toward Ft. Wayne at an average speed of $70$ miles per hour. . Which of the following functions best models Maya’s mile marker position $(M)$ as a function of the hours of elapsed time $(t)$?

$M(t) = −50t + 299$

$M(t) = 50t + 299$

$M(t) = −50t -299$

$M(t) = 50t - 299$

$Q_{2}:$ Omar travels home from work at a constant speed. Ten minutes after leaving work he is $20$ miles from home, and $20$ minutes after leaving work he is $12$ miles from home. If he continues to travel at the same speed, Which of the following functions best models Omar's time to arrive home from work is?

$T(x) = 0.8 x + 28$

$T(x) = - 0.8 x + 28$

$T(x) = - 0.8x - 28$

$T(x) = -8 x + 28$

$Q_{3}:$ To join Eastlake Country Club one must pay $d$ dollars for a one time membership fee and pay $w$ dollars for a monthly fee. If the first month is free for the club, what is the total amount, $y$ , $x$ months after a person joined the club, in terms of $d $, $w$ , and $x$ ?

$y= wx-1+ d$

$y= w(x-1)+ d$

$y= d(x-1)+ w$

$y= dx-1+ w$

$Q_{4}:$ Ahmad bought $c$ candies at a price of $70$ cents each. He sold all but $k$ candies at a price of $1.25£$, and made a profit of $p$ dollars. Which of the following represents $p$ in terms of $c$ and $k $?

$p=1.25( c-k)-0.7 c$

$p=1.25 c -0.7 k$

$p=1.25c - 0.7 ( c-k)$

$p=1.25( c-k)-0.7 k$

$Q_{5}:$ A factory produces parts on two eight-hour shifts per day. Each shift produces the parts at a different, but constant, rate. The number of parts produced by each shift are added to obtain a cumulative total for the day. If the cumulative number of parts produced by the end of two hours of the second shift was 320 and the cumulative number produced by the end of five hours of the second shift was 440. Which of the following function represent the parts per hour did the first shift produce?

$y-4x=160$

$y+4x+160=0$

$y-4x-160=0$

$y+4x=160$

$Q_{6}:$ Last week, Karem practiced piano p minutes each day for 5 days, and Carla practiced cello c minutes each day for 6 days. Which of the following represents the total number of minutes Karem and Carla practiced their instruments last week?

$11pc$

$30pc$

$5p+6c$

$6p+5c$

$Q_{7}:$ The number of members that joined the Spanish club between 2000 and 2010 is twice the number of members who joined between 1990 and 2000. If 17 members joined the Spanish club between 1990 and 2000 and m members joined between 2000 and 2010, which of the following equations is true?

$17m=2$

$2m=17$

$m+2=17$

$\frac{m}{2}=17$

$Q_{8}:$ A pet supplies store maintains an inventory of a certain brand of dog food in 15-pound and 30-pound bags. The store pays $0.60 per pound for the 15-pound bags and $0.50 per pound for the 30-pound bags. The store’s current inventory of this product is 32 bags of this dog food for which it paid $408. Which of the following systems of equations can be used to determine the number of 15-pound bags, s, and the number of 30-pound bags, b?

$s+d=32$ and $9s+15b=408$

$s+d=32$ and $15s+30b=408$

$s+d=45$ and $9s+15b=408$

$s+d=408$ and $15s+30b=32$

$Q_{9}:$ The graph below represents the solution set to the inequality:

$y<\frac{1}{4} x-3$

$4 y < \frac{1}{4} x-3$

$y < 4 x-3$

$y<\frac{1}{4} x + 3$

$Q_{10}:$ When the stadium, which has seating capacity up to 70,000, opened to the public two hours before the game, there were 35,215 spectators at the stadium. Each minute after, the number of spectators increased by 230. If t represents the time, in minutes, after the stadium opened, which of the following inequalities represents the range of minutes when the stadium is at or above capacity?

$ 70,000 − 230 \leq t$

$ 70,000 \leq 230 t$

$ 70,000 − 230t \geq 35,215 $

$35,215 + 230t \geq 70,000 $

$Q_{11}:$ Joaquin receives a commission of $35 for every desktop computer system that he sells and $25 for every laptop computer. His goals for the month were to sell more than 60 computers and to earn at least $1,600 in commissions. Joaquin exceeded his commission goal, but fell short of reaching his goal for the number of computers sold. Which of the following systems of inequalities describes the number of desktop computers, d, and laptop computers, p, that Joaquin sold?

$d+p\leq 59$, $35d+25p>1,600$

$d+p\leq 60$, $25d+35p>1,600$

$d+p\leq 60$, $35d+25p>1,600$

$d+p< 60$, $35d+25p \geq 1,600$

$Q_{12}:$ If (0, 0) is a solution to the given system of inequalities, which of the following relationships must be true?

$p>q$

$|p| > |q|$

$p=-q$

$Q_{13}:$ Malak’s cellular phone company charges $30£$ per month plus $3£$for every gigabyte or portion thereof for data usage. If Maria does not want to spend more than $50£$ this month, which the following inequality that represent the maximum data, in gigabytes, she can use?

$ 30 + 3g \leq 50$

$ 30 + 3g < 50$

$ 30 + 3g > 50$

$ 30 + 3g \geq 50$

$Q_{14}:$ Which of the following equations has represent graph below?

$y = 1.6x + 0.8$

y = 1.6x - 0.8

y = 16x + 8

y = 16x -8

$Q_{15}:$ The graph of line g is shown below. Which equation represent it?

$y = -0.5x - 4$

$y = 0.5x + 4$

$y = -0.5x + 4$

$y = -0.5x + 0.4$

$Q_{16}:$ Which of the following equations has represent graph below?

$y=2x+4$

$-y=-2x+4$

$y=-2x-4$

$y=-2x+4$

$Q_{17}:$ Which of the following inequality has represent graph below?

$y \leq -2x+4$

$y \geq -2x+4$

$y > -2x+4$

$y < -2x+4$

$Q_{18}:$ Which of the following inequality has represent graph below?

$y \leq 3x+6$

$y \geq 3x+6$

$y > 3x+6$

$y < 3x+6$

$Q_{19}:$ Jana is selling cookies and brownies for a fundraiser. Each brownie is $2.50£$ and each cookie is $1.85£$. Jana wants to make at least $80£$ and sell at minimum $10$ brownies. which of the following inequality models the word problem?

$2.50 b+1.85c \leq 80$

$2.50 b+1.85c \geq 80$

$2.50 c+1.85b \geq 80$

$2.50 c+1.85b \leq 80$

$Q_{20}:$ The sum of $120k$ and $215 j$ does not exceed $2,500$. Which of the following inequalities represents the statement above?

$120k+215j <2,500$

$120k+215j > 2,500$

$120k+215j \leq 2,500$

$120k+215j \geq 2,500$

$Q_{21}:$ On January 1, 2000, Jon had 2,000 baseball cards and Basel had 1,000 baseball cards. If Jon adds 150 cards per year to his collection and Basel adds 220 cards per year to his collection. Among the following inequalities, which one determines the earliest year when Basel will have more cards than Jon?

$1000 + 220x > 2000 + 150x $

$1000 + 220x = 2000 + 150x $

$1000 + 220x < 2000 + 150x$

$1000 + 220x \leq 2000 + 150x$

$Q_{22}:$ In Beach, you can take a luxury golf cart ride around downtown. The driver charges $4£$ for the first $\frac{1}{4}$ mile, plus $1.50£$ for each additional $\frac{1}{2}$ mile. Which inequality represents the number of miles $m$, that you could ride and pay no more than $10£$?

$ 3.25 + 1.5 m \leq 10$

$3.25 + 3m \leq 10$

$ 4 + 1.5m \leq 10$

$ 4 + 3m \leq 10$

$Q_{23}:$ You are planning to sell handmade candles. You estimate that your fixed monthly costs (rent, utilities, etc.) amount to $\$ 500$, and you can produce each candle for $\$ 3$. You plan to sell each candle for $ \$ 8$. Which of the following represents the profit $(P)$ you make from selling $x$ candles?

$P = 3x + 8$

$P = 5x - 3 $

$P = 8x - 3 $

$P = 3x - 5$

$Q_{24}:$ You want to buy concert tickets for you and your friends. The tickets cost $\$ 30$ each, and you can only spend a maximum of $\$ 150$. How many tickets $(x)$ can you buy without exceeding your budget?

$x \leq 3$

$ x \qeq 3$

$x \leq 5$

$x \geq 5$

$Q_{25}:$ You are considering two job offers. Job A pays a fixed salary of $\$ 40,000$ per year, while Job $B$ offers a fixed salary of $\$ 30,000$ per year plus a commission of $\$ 200$ for each sale made. You want to find out how many sales $(x)$ you need to make for Job $B$ to be a better option in terms of income. Which of the following represents the inequality for this situation?

$30,000x > 40,000$

$30,000 + 200x > 40,000$

$30,000 + 200x < 40,000$

$30,000x < 40,000$

Name