Solving Real Word Problems

A metalsmith is mixing two molten metals, each containing different percentages of silver. The table shows the amount of each molten metal used. Which two expressions are both equivalent to t, the total number of grams in the mixture?

A. (15)(0.75) and 0.7(15 - x) + 0.9x

A chemist mixes 4 liters of one acid solution with 10 liters of a 40% solution, resulting in a 30% acid solution. The table shows the amount of each solution used. What is the value of x, the acid concentration of the first solution?

A. 0.05

The volume, V, of a rectangular prism is determined using the formula , where l is the length, w is the width, and h is the height of the prism. Carltren solves for w and writes the equivalent equation w = . Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches?

4.5 inches

Four ounces of oregano and 2 ounces of garlic powder are mixed to create a poultry seasoning. Oregano costs $4 per ounce, and garlic powder costs $3 per ounce. The table shows the costs of the ingredients. What is the value of y in the table?

6

The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s = 180(n - 2), where n is the number of sides. Benita solves this equation for n and writes the equivalent equation n = + 2. Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°?

9 sides

Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average speed of 20 miles per hour. The entire two-part, 15-mile race took him 1.125 hours to complete. Which table correctly represents his rates, times, and distances for each part of the race?

A.

Marta is solving the equation S = 2Πrh + 2Πr2 for h. Which should be the result?

A.

Solve for w. 5w + 9z = 2z + 3w

A.

Working together, Melissa and Jing can mow a lawn in 5 hours. It would take Melissa 8 hours to do the job alone. What is the value of r, the part of the lawn that Jing could complete in 1 hour?

A. 0.075

Working together, Shawn and Hector can install a tile floor in 6 hours. It would take Shawn 9 hours to do the job alone. What is the value of r, the part of the tile that Hector could install in 1 hour?

A. 1/18

If Jasper installs a floor himself, it will take him 7 hours. Working with Yolanda, it will take them 3 hours. If they work together, what is the missing value in the table that represents the part of the floor Jasper will install?

A. 1/7(3)

Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B contains an unknown percentage of blue pigment. The mixture of the two inks contains 35% blue pigment. What percentage of blue pigment is in ink B?

A. 45%

The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is

A. C = K - 273.15

It would take Marco 6 hours to paint a fence by himself. It would take Jaylyn 5 hours to paint the same fence by herself. Marco is creating this table to help him determine how long it would take them to paint the fence together. Which heading should be written above the first column of numbers?

A. Rate (part/hour)

The amount of potential energy, P, an object has is equal to the product of its mass, m, its height off the ground, h, and the gravitational constant, g. This can be modeled by the equation P = mgh. What is the equivalent equation solved for h?

B.

The axis of symmetry for a quadratic equation can be found using the formula x = , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. When the equation is solved for a, such that b is the numerator of the resulting fraction, what is the denominator of the fraction?

B. -2x

Fifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment. Which equation can be used to solve for x, the total amount of paint in the mixture of the two colors?

B. 0.15(40) + 0.6(x - 40) = 0.25(x)

Working together, Katherine and Marina can sand a large cabinet in 2 hours. It would take Katherine 10 hours to do the job alone. What is the value of r, the part of the job that Marina can complete in 1 hour?

B. 0.4

Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will it take them?

B. 18 minutes

The formula for the area of a triangle is A = bh, where b is the length of the base and h is the height. The equation solved for h is h = . Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.

B. 5 units

It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?

B. 5/8 + 5r = 1

The formula for the circumference of a circle is C = 2r, where r is the radius and C is the circumference. The equation solved for r is r = . Find the radius of a circle that has a circumference of 16.

B. r= 8

The circumference of a circle can be found using the formula C = 2r. Which is an equivalent equation solved for r?

C.

Giuliana has 22 quarters and dollar coins worth a total of $10.75. Which equation can be used to find d, the number of dollar coins Giuliana has?

C. 0.25(22 - d) + d = 10.75

If Judy completes a puzzle by herself, it takes her 3 hours. Working with Sal, it only takes them 2 hours. What is the missing value from the table that represents Judy's rate?

C. 1/3

Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the amount of each solution used. What is the value of x?

C. 10

Four cups of a salad blend containing 40% spinach is mixed with an unknown amount of a salad blend containing 55% spinach. The resulting salad contains 50% spinach. How many cups of salad are in the resulting mixture?

C. 12

The formula to convert °F to °C is C = (F - 32). Convert 50°C to °F.

C. 122F

Tickets to a school production cost $5 for a student ticket and $10 for an adult ticket. A total of 67 tickets were purchased at a cost of $440. Which value could replace c in the table?

C. 67 - a

Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question. There are 15 questions on the test and the students have been given 55 minutes to complete it. Which value could replace x in the table?

C. 8(15 - m)

Solve for a. 7a - 2b = 5a + b

C. a= 3/2b

The slope, m, of a linear equation can be found using the formula m = , where the x- and y-values come from two ordered pairs, and (x1, y1) and (x2, y2). What is an equivalent equation solved for y2?

C. y2 = m(x2 - x1) + y1

If Dominik completes a project by himself, it will take him 8 hours. Working with Katarina, it will take them 5 hours. If they work together, what is the missing value from the table that represents the part of the project Dominik will complete?

D.

Solve the equation for a. K = 4a + 9ab

D.

Alex has 84 quarters and nickels worth a total of $17.80. Which equation can be used to find q, the number of quarters Alex has?

D. 0.05(84 - q) + 0.25q = 17.80

Yuto and Lian are at train stations 1,880 kilometers apart. Yuto boards a train heading east at an average speed of 220 kilometers per hour. At the same time, Lian boards a train heading west on a parallel track at an average speed of 250 kilometers per hour. How far has Lian traveled when the two trains pass each other?

D. 1,000 kilometers

A ride on the roller coaster costs 4 tickets while the boat ride only costs 3 tickets. Michael went on the two rides a total of 10 times and spent a total of 37 tickets. Which equation is true?

D. 4r + 3(10 - r) = 37

The average rate of the first part of Yi's walk on a park loop was 4 miles per hour. She then met up with a friend and the two walked the rest of the way at an average rate of 5 miles per hour. The entire 3-mile walk took Yi 42 minutes (0.7 hour). Which equation can be used to solve for x, the time in hours that Yi spent walking before meeting her friend?

D. 4x + 5(0.7 - x) = 3

The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh a total of 249 ounces. Which value could replace x in the table?

D. 5(45 - h)

Nikita ran a 5-kilometer race in 39 minutes (0.65 of an hour) without training beforehand. In the first part of the race, her average speed was 8.75 kilometers per hour. For the second part of the race, she started to get tired, so her average speed dropped to 6 kilometers per hour. Which expression represents Nikita's distance for the second part of the race?

D. 6(0.65 - t)