24 coloring books, 60 crayons, and 84 markers can be packaged into at most how many identical packages? How many of each would each package contain? First, determine the greatest common factor (GCF) of 24, 60, and 84 using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=24&num2=60&num3=84&pl=GCF']GCF calculator[/URL]. GCF(24, 60, 84) = 12 So we have 12 identical packages. Now, figure out how many coloring books, crayons, and markers for each package [LIST] [*]24/12 = 2 coloring books [*]60/12 = 5 crayons [*]84/12 = 7 markers [/LIST] [B]So we have 12 identical packages, each containing 2 coloring books, 5 crayons, and 7 markers[/B]

7 black shirts 5 white shirts 10 gray shirts one is chosen at random, what is the probability that it is not gray [U]Find the total shirts:[/U] Total shirts = Black Shirts + White Shirts + Gray Shirts Total shirts = 7 + 5 + 10 Total shirts = 22 [U]Calculate the probability of choosing a gray shirt:[/U] P(Gray) = Number of Gray shirts / Total Shirts P(Gray) = 10/22 We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=10%2F22&frac2=3%2F8&pl=Simplify']type in 10/22 into our search engine, choose simplify[/URL], and we get: P(Gray) = [B]5/11[/B]

A box contains 4 plain pencils and 4 pens. A second box contains 5 color pencils and 3 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected? [LIST] [*]First box, P(pen) = 4/8 = 1/2 = 0.5 [*]Second box, P(crayon) = 3/8 [/LIST] Since each event is independent, we have: P(Pen from Box 1) * P(Crayon from Box 2) = 1/2 * 3/8 = [B]3/16 or 0.1875[/B]

A box contains 4 plain pencils and 4 pens. A second box contains 5 color pencils and 3 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected? [LIST] [*]First box, P(pen) = 4/8 = 1/2 = 0.5 [*]Second box, P(crayon) = 3/8 [/LIST] Since each event is independent, we have: P(Pen from Box 1) * P(Crayon from Box 2) = 1/2 * 3/8 = [B]3/16 or 0.1875[/B]

A box contains 5 plain pencils and 3 pens. A second box contains 2 color pencils and 2 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected [U]Calculate the probability of a plain pencil in the first box:[/U] P(plain pencil in the first box) = Total Pencils / Total Objects P(plain pencil in the first box) = 5 pencils / (5 pencils + 3 pens) P(plain pencil in the first box) = 5/8 [U]Calculate the probability of a color pencil in the first box:[/U] P(color in the second box) = Total Pencils / Total Objects P(color in the second box) = 2 pencils / (2 pencils + 2 crayons) P(color in the second box) = 2/4 We can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F4&frac2=3%2F8&pl=Simplify']Type 2/4 into our search engine[/URL] and we get 1/2 Now the problem asks for the probability that a plain pencil from the first box and a color pencil from the second box are selected. Since each event is independent, we multiply them together to get our answer: P(plain pencil in the first box, color in the second box) = P(plain pencil in the first box) * P(color in the second box) P(plain pencil in the first box, color in the second box) = 5/8 * 1/2 P(plain pencil in the first box, color in the second box) = [B]5/16[/B]

A box contains 5 plain pencils and 7 pens. A second box contains 4 color pencils and 4 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected? Probability of plain pencil from first box: 5/(5 + 7) = 5/12 Probability of color pencil from second box: 4/(4 + 4) = 4/8 = 1/2 Probability of both events together: Since each event is independent, we multiply probabilities: 5/12 * 1/2 = [B]5/24[/B]

A cup of coffee cost $4 and a cup of tea cost $3.50. If ray has $40 and has bought 6 cups of coffee, find the maximum cups of tea he can buy [U]Calculate total coffee spend:[/U] Total coffee spend = Cost per Cup of Coffee * Cups of Coffee Total coffee spend = 4 * 6 Total coffee spend = 24 [U]Calculate remaining amount to be spent on tea:[/U] Remaining tea money = Starting Money - Total Coffee spend Remaining tea money = 40 - 24 Remaining tea money = 16 [U]Calculate cups of tea Ray can buy:[/U] Cups of tea Ray can buy = Remaining Tea money / Cost per cup of tea Cups of tea Ray can buy = 16/3.50 Cups of tea Ray can buy = 4.57142857143 Since Ray can't buy partial cups, we round down and we get: Cups of tea Ray can buy = [B]4[/B]

A drawer is filled with 9 black shirts , 6 white shirts, and 5 gray shirts one shirt is chosen at random from the drawer find the probability that it is not a white shirt P(Not White) = P(Black or Gray) P(Black or Gray) = (Total Black + Total Gray)/Total Shirts P(Black or Gray) = (9 + 5)/(9 + 6 + 5) P(Black or Gray) = 14/20 Simplifying this [URL='https://www.mathcelebrity.com/fraction.php?frac1=14%2F20&frac2=3%2F8&pl=Simplify']using our fraction simplify calculator[/URL], we get: P(Black or Gray) = [B]7/10, or 0.7 or 70%[/B]

A spinner has 10 equally sized sections, 2 are gray 8 are blue. The spinner is spun twice. What is the probability that the first spin lands on blue and the second lands on gray? P(blue) = Blue sections / Total Sections P(blue) = 8/10 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F10&frac2=3%2F8&pl=Simplify']Reducing this using our simplified fraction calculator[/URL], we get: P(blue) = 4/5 P(gray) = Gray sections / Total Sections P(blue) = 2/10 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F10&frac2=3%2F8&pl=Simplify']Reducing this using our simplified fraction calculator[/URL], we get: P(gray) = 1/5 We want the probability of blue,gray. Since each spin is independent, we multiply the two probabilities to get our answer: P(blue, gray) = P(blue) * P(gray) P(blue, gray) = 4/5 * 1/5 P(blue, gray) = [B]4/25[/B]

Grayson took a total of 16 quizzes over the course of 8 weeks. How many weeks of school will Grayson have to attend this quarter before he will have taken a total of 20 quizzes? Assume the relationship is directly proportional. Set up a proportion of quizzes to weeks, where w is the number of weeks for 20 quizzes: 16/8 = 20/w [URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=20&den1=8&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get: w = [B]10[/B]

In Trina's desk drawer, there are 15 paper clips and 18 rubber bands. In Kirk's office supply tray, there are 13 paper clips and 16 rubber bands. Who has a higher ratio of paper clips to rubber bands? Trina: 15/18 Kirk: 13/16 We want common denominators to compare, so we get a greatest common factor (GCF) for 16 and 18. [URL='https://www.mathcelebrity.com/gcflcm.php?num1=16&num2=18&num3=&pl=GCF+and+LCM']Running this through our search engine[/URL], we get GCF(16, 18) = 144 For Trina, 144/18 = 8 For Kirk, 144/16 = 9 We multiply Trina's fraction, top and bottom by 8: 15 * 8 / 18 * 8 120/144 We multiply Trina's fraction, top and bottom by 8: 13 * 8 / 16 * 8 104/144 [B]Trina[/B] has more in her numerator, so her ratio of paper clips to rubber bands is greater.

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month? [U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 10% written as a decimal is 0.1. We want decimals to solve equations easier. S(m) = 0.1m + 1500 [U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 15% written as a decimal is 0.15. We want decimals to solve equations easier. S(m) = 0.15m + 1200 [U]The question asks what is m when both S(m)'s equal each other[/U]: The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other 0.1m + 1500 = 0.15m + 1200 We want to isolate m terms on one side of the equation. Subtract 1200 from each side: 0.1m + 1500 - 1200 = 0.15m + 1200 - 1200 Cancel the 1200's on the right side and we get: 0.1m - 300 = 0.15m Next, we subtract 0.1m from each side of the equation to isolate m 0.1m - 0.1m + 300 = 0.15m - 0.1m Cancel the 0.1m terms on the left side and we get: 300 = 0.05m Flip the statement since it's an equal sign to get the variable on the left side: 0.05m = 300 To solve for m, we divide each side of the equation by 0.05: 0.05m/0.05 = 300/0.05 Cancelling the 0.05 on the left side, we get: m = [B]6000[/B]

Mrs. Evans has 120 crayons and 30 pieces of paper to give her students. What is the largest number of students she can have her class so that each student gets an equal number of crayons and equal number of paper? [URL='https://www.mathcelebrity.com/gcflcm.php?num1=30&num2=120&num3=&pl=GCF+and+LCM']Using our GCF calculator for the GCF(30, 120)[/URL], we get 30. So 30 people get the following: [B]30/30 = 1 piece of paper 120/30 = 4 crayons[/B]

Free Multiplication Array Calculator - This allows you to enter pictorials using * symbols to represent multiplication

Murray makes $12.74 per hour. How much does he earn in 38 hours? [U]Calculate Earnings:[/U] Earnings = Hourly Rate * Number of hours worked Earnings = $12.74 * 38 Earnings = [B]$484.12[/B]

Roger has 9 white buttons. He has 3 fewer brown buttons than white buttons. Roger has 3 more gray buttons than brown buttons. How many buttons does Roger have in all? [LIST] [*]9 white buttons [*]3 fewer brown buttons than white buttons. So Brown = 9 white - 3 = 6 brown [*]Gray = 3 more than brown = 6 + 3 = 9 [/LIST] All together: 9 white + 6 brown + 9 gray = [B]24 buttons[/B]

Free What is a Ray Calculator - This lesson walks you through what a Ray is and the various implications of a ray in geometry