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This Lesson (Solving arithmetic word problems by reasoning) was created by by ikleyn(52847)
  About ikleyn: Solving arithmetic word problems by reasoningProblem 1An advertisement from the back of Denton checklist:(1) $1300 sofa and love seat (2) $1400 sofa and two chairs (3) $1600 sofa, love seat, one chair How much does each piece of furniture cost individually? Solution From (1) and (3), we see that one chair price is 1600 - 1300 = 300 dollars. Having it, from (2) we conclude that the sofa price is 1400 - 2*300 = 1400 - 600 = 800 dollars. Finally, from (1) we deduce that the love seat price is 1300 - 800 = 500 dollars. ANSWER. The prices are $800 for sofa, $500 for love seat and $300 for a chair. Problem 2Ben earns 20 cents for every card he sells. When he sells a whole box of 12 cards he earns an extra $2.How many cards does he need to sell to earn $332 ? Solution According to the problem, Ben earns 12*20 cents PLUS 2 dollars = 4.40 dollars for every box of 12 cards sold. So we divide $332 by $4.40 to get Problem 3The ratio of the number of blue sticks to the number of green sticks in a box was 4:1.When David took out some blue and sticks and replaced them with an equal number of green sticks, the ratio of the number of blue sticks to the number of green sticks became 3:1. If there were 185 green sticks in the box now, (a) find the total number of blue and green sticks in the box, (b) find the number of green sticks in the box at first. Solution This problem is good for mental solution, if to solve it in a backward manner.
According to the condition, in the final state, there are 185 green sticks in the box,
and the number of blue sticks is thrice of it, i.e. 185*3 = 555.
Thus the total number of sticks in the final state is 185 + 555 = 740.
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| Now notice that total number of sticks in the final state |
| is THE SAME as at the beginning, according to the problem. |
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HENCE, there were 740 sticks in the box at the beginning, and the ratio of blue to green sticks was 4:1.
So, there were 4+1 = 5 equal groups; each group contained 740/5 = 148 sticks.
Thus the problem is just solved: at the beginning, there were 148 green sticks and 148*4 = 592 blue sticks.
ANSWER. (a) There were 740 sticks in the box, in total (the same number at the beginning and at the end).
(b) There were 148 green sticks in the box at first.
Problem 4Marty’s age is 36, which is 12 more than 4 times Daisy’s age. How old is Daisy?Solution Solve it MENTALLY in 2 steps, using backward method.
Step 1. Subtract 12 from 36 to get 36-12 = 24.
Step 2. Divide 24 by 4 to get 24/4 = 6.
ANSWER. Daisy is 6 years old.
This method is good for the second grade students, who just can subtract and divide integer numbers, but did not learn equations, yet. My other lessons on arithmetic word problems in this site are Arithmetic word problems to solve them MENTALLY Simple arithmetic word problems solved in a right way Arithmetic coin problems Simple arithmetic word problems on "rate of work" Simple and simplest arithmetic Travel & Distance problems Typical arithmetic Travel & Distance problems Entertaining catching up arithmetic Travel & Distance problems Other basic arithmetic Travel & Distance problems Advanced arithmetic word problems on Travel & Distance Finding travel time and average rate Flying back and forth OVERVIEW of the first group of lessons on arithmetic word problems To see the whole list of lessons on arithmetic problems, use this link Arithmetic problems - YOUR ONLINE TEXTBOOK It is your way to the entry page of the online textbook on Arithmetic problems. This lesson has been accessed 1681 times. |
