Q&A for How to Solve Word Problems in Algebra

Carefully read the problem and figure out what information you're given and what that information should be used for. Once you know what you need to do with the values they've given you, the problem should be a lot easier to solve.

Let x = Deborah's money. Then (x - 27) = Colin's money. That means that (x) + (x - 27) = 150. Combining terms: 2x - 27 = 150. Adding 27 to both sides: 2x = 177. So x = 88.50, and (x - 27) = 61.50. Deborah has $88.50, and Colin has $61.50, which together add up to $150.

Let x be Bob's current age. Then Karl's current age is 2x. Nine years ago Bob's age was x-9, and Karl's age was 2x-9. We're told that nine years ago Karl's age (2x-9) was three times Bob's age (x-9). Therefore, 2x-9 = 3(x-9) = 3x-27. Subtract 2x from both sides, and add 27 to both sides: 18 = x. So Bob's current age is 18, and Karl's current age is 36, twice Bob's current age. (Nine years ago Bob would have been 9, and Karl would have been 27, or three times Bob's age then.)

Let b equal the length of the base. Then the height is (2b + 4). The area is 35 = [(b)(2b + 4)] / 2 = [2b² + 4b] / 2 = b² + 2b. Then b² + 2b -35 = 0. So (b +7)(b - 5) = 0. That means b = -7 or 5. The length of the base cannot be a negative number, so the base is 5 inches. That makes the height 14 inches. (To check the answer: [(5)(14)]/2 = 70/2 = 35.)

(.2)(30) = 6.

(.15)(20) = 3.

A good approach is to set up two equations: N(t) = ($10/hour)*t is the annual cost to a nonmember who uses a court for an unknown time (t) and M(t) = $300 + ($4/hour)*t is the corresponding cost function for members. You want to solve M(t) < N(t) for t so, $300 + ($4/hour)*t < ($10/hour)*t becomes $300 < ($10/hr)t - ($4/hr)t becomes $300 < ($6/hr)t becomes $300/($6/hr) < t finally becomes 50 hours < t. So 50 hours is the break even point where both members and nonmembers pay $500, any higher and members pay less.

Let x be the number of miles Josephine ran. Then (x-6) is the number of miles Steve ran. Their total, 42, can be represented by x + (x-6). So x + (x-6) = 2x - 6 = 42. Add 6 to both sides: 2x = 48, and x = 24.

Let x be the first share. Then (x - 50) is the second share, and (x - 50 - 100) or (x - 150) is the last share. Add them together: (x) + (x - 50) + (x - 150) = 3x - 200 = 850. Solve for x by adding 200 to both sides and then dividing both sides by 3: x = £350.00. (To check the answer: 350 + 300 + 200 = 850.)

The first time they will flash together is 4 x 9 = 36 minutes after they begin rotating. 36 is the lowest multiple of 4 that is also a multiple of 9.

A 26.3% increase means the 2011 sales figure is 126.3% of the 2010 figure. If you divide the 2011 figure by 126.3%, you'll get the 2010 figure: (324,402) / 126.3% = 324,402 / 1.263 = 256,850.

Assume $1155.60 is the total revenue for all tickets sold. Let x be the number of child tickets sold. Then 4x is the number of adult tickets sold. The equation is (5.20)(x) + (9.40)(4x) = 1155.60. (5.2 x) + (37.6 x) = 42.8 x = 1155.6. x = 27. To check, (27)(5.20) + (108)(9.40) = 140.40 + 1015.20 = 1155.60. There were 27 child tickets sold.

Let x equal the amount invested in the 3% account. Then .03x is the amount yielded by the 3% account in a year. The amount invested in the 14% account can be represented by 32,000 - x. So (.14)(32000 - x) is the amount yielded by the 14% account. Make an equation setting the sum of those two yields equal to $2280, and solve for x.

Let x be the number. Then 12.6 - x = 5.4. Add x to both sides, and subtract 5.4 from both sides: 7.2 = x.

Let x be Lee's age. Then Timothy's age is (x - 2), and (x)(x - 2) = x² - 2x = 120. So x² - 2x -120 = 0. Factor the left side: (x + 10)(x - 12) = 0. That means x = either -10 or 12. Lee can't be -10 years old, so he must be 12 years old (and Timothy is (12 - 2) = 10 years old).

That question doesn't make any sense. If Sarah is today 25 years older than Gavin, on this same date every year she will always be 25 years older than Gavin.

Let the numbers be x and (x - 6). Then (x)(x - 6) = -8. So x² - 6x = -8, and x² - 6x + 8 = 0, or (x - 4)(x - 2) = 0. So x = 2 or 4, and (x - 6) = -4 or -2. Now look for a pair of numbers that satisfies the requirements of the question: two pair of numbers do that: 2 and -4, and 4 and -2. So there are two valid answers to the question.

Let v be Vatha's age and c be Chris's age. We're given that v + c = 36. In four years, v + c will equal 36 + 4 + 4 = 44 (adding four years to each current age). We're given that 44 = 2v. Then v = 22, and c = 36 - v = 36 - 22 = 14.

Divide 6/7 by 3/14. 6/7 ÷ 3/14 = (6/7)(14/3) = 84/21 = 4. Together they can paint four full pictures in an hour.