Consecutive means one after the other. Note: we could have also tried "guess and check": But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12). See Lesson 1, Problem 8.Yet, word problems fall into distinct types. Below are some examples. There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 So 10 tables would take Sam just 20 days. Let's first make a sketch so we get things right! You may be asked to find the Value of a Particular Term or the Pattern of a Sequence Proportion Problems involve proportional and inversely proportional relationships of various quantities. Let's start with a really simple example so we see how it's done: Formula for Area of a Rectangle: A = w × h. Now let's try the example from the top of the page: We know that Sam played 4 more games than Alex, so: S = A + 4, And we know that together they played 12 games: S + A = 12, We are being asked for how many games Alex played: A. : We are being asked for the length of the room: L. This is a quadratic equation, there are many ways to solve it, this time let's use factoring: There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative! 30 days of Alex alone is also 10 tables: 30a = 10. Word problems on ages. Examples. Time and work word problems. So there are now 12 girls and 16 boys in the class, making 28 students altogether. Distance, Rate, and Time Word Problems These Algebra 1 Equations Worksheets will produce distance, rate, and time word problems with ten problems per worksheet. So Joelâs normal rate of pay is $12 per hour, Joelâs normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. Turn the English into Algebra: Letters: Use a for Alex's work rate; Use s for Sam's work rate; 12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10. 3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours, We need to rearrange the formula to find the area. These Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade. Other algebra word problems/related topics: Homepage. Note that Using Systems to Solve Algebra Word Problems can be found here in the Systems of Linear Equations and Word Problems section. First work out s using the volume formula: We are being asked for Joel's normal rate of pay $N. Add, subtract, multiply, and divide to solve these decimal word problems. And they are even, so they could be 2 and 4, or 4 and 6, etc. We know there are seven days in the week, so: d + e = 7, And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27, We are being asked for how many days she trains for 5 hours: d. Check: She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week. We will call the smaller integer n, and so the larger integer must be n+2. At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1. In Algebra we often have word questions like: On the weekend Sam played 4 more games than Alex did, and together they played 12 games. Ratio and proportion word problems. You may select the numbers to be represented with digits or in words. I hope these examples will help you get the idea of how to handle word questions. Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. the width of the room is half its length: the total area is the (room width + 3) times the length. We are being asked how long it would take Sam to make 10 tables. WORD PROBLEMS. Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES. Word problems on constant speed. The trick is to break the solution into two parts: To turn the English into Algebra it helps to: You should also write down what is actually being asked for, so you know where you are going and when you have arrived! So there are two solutions: −14 and −12 is one, 12 and 14 is the other. Using the Quadratic Equation Solver we get −14 and 12. Example 1. ax ± b = c. All problems like the following lead eventually to an equation in that simple form. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660, More about Money, with these two examples involving Compound Interest, We are being asked for the Future Value: FV, We are being asked for the Interest Rate: r, Check: $1,000 × (1.05)9 = $1,000 × 1.55133 = $1,551.33, At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1, Which can be rearranged to b + 4 = 2(g − 2), We are being asked for how many students there are altogether now: b + g, And 3b = 4g, so b = 4g/3 = 4 × 12 / 3 = 16, so there are 16 boys. W ORD PROBLEMS require practice in translating verbal language into algebraic language. 10. 30a = 10, so Alex's rate (tables per day) is: a = 10/30 = 1/3, Which means that Sam's rate is half a table a day (faster than Alex!). Word problems on sets and venn diagrams. Problems. add, total, sum, increase, more, combined, together, plus, more than, minus, less, difference, fewer, decreased, reduced, multiplied, times, of, product, factor, divided, quotient, per, out of, ratio, ratio, percent, rate.