Lines
3a + 4b = 25
A shipping company charged a customer $25 to ship some small boxes and some large boxes. The equation above represents the relationship between a, the number of small boxes, and b, the number of large boxes, the customer had shipped. If the customer had 3 small boxes shipped, how many large boxes were shipped?
A. 3
B. 4
C. 5
D. 6
B. 4
A clothing store is having a sale on shirts and pants. During the sale, the cost of each shirt is $15 and the cost of each pair of pants is $25. Geoff can spend at most $120 at the store. If Geoff buys s shirts and p pair of pants, which of the following must be true?
A. 15s + 25p <= 120
B. 15s + 25p >= 120
C. 25s + 15p <= 120
D. 25s + 15p >= 120
A. 15s + 25p <= 120
Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4 shirts and 2 pants for $86, and Sofia purchased 3 shirts and 5 pairs of pants for $166. Which of the following systems of linear equations represents the situation, if x represents the price in dollars, of each shirt and y represents the price, in dollars, of each pair of pants?
A. 4x + 2y = 86 and 3x + 5y= 166
B. 4x + 3y = 86 and 2x + 5y= 166
C. 4x + 2y = 166 and 3x + 5y= 86
D. 4x + 3y = 166 and 2x + 5y= 86
A. 4x + 2y = 86 and 3x + 5y= 166
If 5(x+4) = 4(x+4) + 29, what is the value of x+4?
A. -4
B. 25
C. 29
D. 33
C. 29
A total of 364 paper straws of equal length were used to construct two types of polygons: triangles and rectangles. The triangles and rectangles were constructed so that no two polygons had a common side. The equation 3x + 4y = 364 represents this situation, where x is the number of triangles constructed and y is the number of rectangles constructed. What is the best interpretation of (x, y) = (24, 73) in this context?
A. If 24 triangles were constructed, then 73 rectangles were constructed.
B. If 24 triangles were constructed, then 73 paper straws were used.
C. If 73 triangles were constructed, then 24 rectangles were constructed.
D. If 73 triangles were constructed, then 24 paper straws were used.
A. If 24 triangles were constructed, then 73 rectangles were constructed.
An event planner is planning a party. It costs the event planner a onetime fee of $35 to rent the venue and $10.25 per attendee. The event planner has a budget of $200. What is the greatest number of attendees possible without exceeding the budget?
16
A petting zoo sells two types of tickets. The standard ticket, for admission only, costs $5. The premium ticket, which includes admission and food to give to the animals, costs $12. One Saturday, the petting zoo sold a total of 250 tickets and collected a total of $2,300 from ticket sales. Which of the following systems of equations can be use to find the number of standard tickets, s, and premium tickets, p, sold on that Saturday?
A. s + p = 250 and 5s + 12p = 2,300
B. s + p = 250 and 12s + 5p = 2,300
C. 5s + 12p = 250 and s + p = 2,300
D. 12s + 5p = 250 and s + p = 2,300
A. s + p = 250 and 5s + 12p = 2,300
3/17 or .1765
On a 210-mile trip, Cameron drive at an average speed of 60 miles per hour for the first x hours. He then completed the trip, driving at an average speed of 50 miles per hour for the remaining y hours. If x = 1, what is the value of y?
y = 3
A certain elephant weights 200 pounds at birth and gains more than 2 but less than 3 pounds per day during its first year. Which of the following inequalities represents all possible weights, w, in pounds, for the elephan 365 days after birth?
A. 400 < w < 600
B. 565 < w < 930
C. 730 < w < 1,095
D. 930 < w < 1,295
D. 930 < w < 1,295
A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-person tents?
A. 30
B. 20
C. 19
D. 18
C. 19
In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the point (2, 2). If the point (20, w) lies on the line k, what is the value of w?
74
A band member earns $500 for the first four concerts performed during a given month. The band member earned a total of $900 for playing 6 concerts in a month. Which function g gives the total earnings, in dollars, for x concerts, where x >= 4?
A. g(x) = 150x
B. g(x) = 150x +150
C. g(x) = 200x - 300
D. g(x) = 200x + 500
C. g(x) = 200x - 300
The formula above is the Ohm's law for an electric circuit with current I, in amperes, potential difference V, in volts, and the resistance R, in ohms. A circuit has a resistance of 500 ohms, and its potential difference will be generated by n six-volt batteries that produce a total potential difference of 6n volts. If the circuit is to have a current of no more than 0.25 ampere, what is the greatest number, n, of six-volt batteries that can be used?
20
A vendor sells bags of popcorn at $2.00 each and soda bottles at $1.50 each.
She sells 80 items total, and makes $140.00.
How many of each item were sold?
40 popcorn bags
40 soda bottles
Line p is defined by 4y + 8x = 6. Line r is perpendicular to the line p in the xy-plane. What is the slope of line r?
.5 or 1/2
A certain product costs a company $65 to make. The product is sold by a sales person who earn a commission that is equal to 20% of the sales price of the product. The profit the company makes for each unit is equal to the sales price minus the combined cost of making the product and the commision. If the sales price of the product is $100, which of the following equations gives the number of units, u, of the product the company sold to make a profit of $6,840?
A. (100 (1 - 0.2) - 65) u = 6,840
B. (100 - 65)(1 - 0.8) u = 6,840
C. 0.8(100) - 65u = 6,840
D. (0.2(100) + 65)u = 6,840
A. (100 (1 - 0.2) - 65) u = 6,840
Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?
A. 38
B. 33
C. 22
D. 16
C. 22
During a month, Morgan ran r miles at 5 miles per hour and biked b miles at 10 miles per hour. She ran and biked a total of 200 miles that month, and she biked for twice as many hours as she ran. What is the total number of miles that Morgan biked during the month?
A. 80
B. 100
C. 120
D. 160
D. 160
In the given equation, k is a constant. The equation has no solution. What is the value of k?
3(kx + 13) = 48/17 x +36
16/17 or .9411