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Topic: **Four steps in problem solving****Question:**
Hi i am working on some mind boggling word problems for my algebra class and there are a few i just cant seem to get a grasp on. can someone pleeeeeeeeease help me out, itll be greatly appreciated...
1. Suppose that one slice of mincemeat pie has as many calories as six ounces of pot roast and a piece of chocolate fudge. Suppose that a piece of chocolate fudge has six calories more than four ounces of pot roast. Suppose that one slice of mincemeat pie and nine ounces of pot roast has 944 calories. How many calories would be in one piece of fudge?
2. Suppose there are 20 people around the banquet table, including your self. Suppose one person who is sitting at the head of the table weighs the least and that going around the table, each person weighs 3 pounds more than the previous person. If the combined weight of all the people is 2 tons, find the weight of the person at the head of the table.
3. Suppose 5 cooks, all working at the same speed can peel 7 potatoes all the same size in 3 minutes. How long would it take 7 cooks to grate 21 potatoes? Please answer in minutes and seconds.

July 18, 2019 / By Bridget

1. The first step is to convert the problem into mathematical equations. Doing so yields this: M=6R+F F=4R+6 M+9R=944 where M=calories in one slice of Mincemeat pie, R=calories in one ounce of pot Roast, and F=calories in one piece of chocolate Fudge. The next step is solving for F, which is the answer to the problem. You have three equations and three unknowns, so you can solve this like you would any other system of equations. If my math is correct, F should be 3866/19 or 203.474. 2. Turning the problem into an equation results in this: 2 tons (assuming it means short tons)=4000 pounds=x+(x+3)+(x+6)+ . . . +(x+57)=20x+570 where x=weight in pounds of the person at the head of the table. Simplifying results in x=171.5 pounds. 3. Based on the given information, one cook peels potatoes at a rate of .4667 potatoes/min. If you have 7 cooks that need to peel 21 potatoes, then each cook would peel three potatoes. One cook can peel three potatoes in 6.428 minutes or 6 minutes and 26 seconds, and this is the answer to the question because the 7 cooks each peel their 3 potatoes at the same time resulting in 21 peeled potatoes.

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Let L = length of leader and F = length of fishing rod. Since the leader is 2 ft shorter than the rod, L = F - 2. Since the product of the length of the leader and the length of the rod is 16 (the strength of the line in lbs) you need to find the solution to the equation F x L = F x (F - 2) = 16. This is a quadratic equation so put it in standard form: F^2 - 2F = 16 so F^2 - 2F - 16 = 0. If you try to solve this by factoring, this is the same as coming up with two whole numbers which differ by 2 and multiply to 16, the terms of the problem. The factors of 16 are 4x4, 2x6, and 16x1, none of these differ by 2, so you can't solve by factoring and you will have to put this into the quadratic formula.... F = (-1 +/- sqrt ((-2)^2 - (4x 1 x -16)) / (2x1) ...= (-1 +/- sqrt (4 + 64))/2 ...= (-1 +/- sqrt (68))/2 BTW, you CAN do word problems if you understand them. Here's a link to help you understand how to do them... http://www.purplemath.com/modules/transl... See also the other topics under the heading solving word problems http://www.purplemath.com/modules/index.... see also http://www.purplemath.com/modules/why_ma... PS -- Cattbarf, below, has a more elegant solution, involving completing the square. For info on how to do this, see... http://www.purplemath.com/modules/sqrquad.htm

That's a fine kettle of fish. Let Y be the length of the leader. The length of the rod is Y+2. "If the product,......" (Y)(Y+2)=16 Pushing stuff around Y^2+2Y-16= 0 Solving... (Y+1)^2 = 17 (this is a complete the square routine,which is easier to do than grinding out the quadratic with these numbers) Y+1 = +/- sqrt 17 we dont need the negative root, so Y= sqrt(17)-1 Then Y (which is what we want) is appx 3.12 ft.

13. My gas budget is $125.00 for the month . I drove my Geo 675 miles last month and my Expedition 525 miles. I went over my budget by $25 and paid $3.00 a gallon for gas. My Geo gets 30 miles more per gallon than my Expedition. What mileage does my Expedition get? g = e + 30 ( 675 / g + 525 / e ) * 3 = 125 + 5 675 / ( e + 30) + 525 / e = 130 / 3 e = 17.94570618 g = 47.94570618

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