TWO PROBLEM SOLVING WITH EQUATIONS (using x if needed) GIVING 10 POINTS TO BEST ANSWER AND SHOW YOUR WORK.?
1. The sum of 180$ was divided among 3 people so that the second person received $6 less than twice as much as the first, and the third received $7 more than the second. How much did each person receive ?
2. Stanley worked 6 more than twice as many hours as Kathleen did. How many hours did each work if together they worked 69 hours ?
1. $180 among 3 people. 1st person is x. 2nd has less than twice of 1st, so 2x-6. 3rd has received 7 more than the 2nd, so (2x-6)+7=2x+1
180= x + (2x-6) + (2x+1)
180= 5x-5
185=5x
x=$37. First person
2x-6=(2)(37)-6=$68. Second person.
2x+1=(2)(37)+1= $75 Third Person.
2) Kathleen worked x hours. Stanley worked 6 more than twice as many as Kathleen. 2x+6
Total they had 69 hours.
x+2x+6=69
3x=63
x=21. Kathleen worked 21 hours.
2(21)+6=48. Stanley worked 48 hours.
July 10th, 2010 at 8:08 am
1. $180 among 3 people. 1st person is x. 2nd has less than twice of 1st, so 2x-6. 3rd has received 7 more than the 2nd, so (2x-6)+7=2x+1
180= x + (2x-6) + (2x+1)
180= 5x-5
185=5x
x=$37. First person
2x-6=(2)(37)-6=$68. Second person.
2x+1=(2)(37)+1= $75 Third Person.
2) Kathleen worked x hours. Stanley worked 6 more than twice as many as Kathleen. 2x+6
Total they had 69 hours.
x+2x+6=69
3x=63
x=21. Kathleen worked 21 hours.
2(21)+6=48. Stanley worked 48 hours.
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July 10th, 2010 at 8:39 am
I don’t like to give out answers, but I will do my best to help. You will have to figure on your own.
1. You know the sum = $180. First you will have to show how much $ each person has by using X. For example, if I have three dollars less than 5 times the amount Sarah has (let’s say she has 2X dollars), then I would have 5*2X – 3. You multiply 5 times 2X then subtract 3. Do this for each amount. You will need to make an equation showing each person’s money plus each other and then = 180. Then solve for X. BUT you are not finished. Don’t forget to plug X in to each person’s amount and THEN you will get how much each person had. To check – add all three amounts together and get 180.
2. Kathleen’s hours will be X. Use the same type of format I explained above to solve this one but you will only have 1 X…. It is much easier than the above one. Set the equation up = 69. Solve for X. X will be Kathleen’s hours, then plug X into the simple equation (the one before the = sign) you have for Stanley to get his house.
I know this isn’t what you wanted, but I hope it helps.
References :
July 10th, 2010 at 9:29 am
Let x equal what the first person got. You do this because the problem tells you that the 2nd person relates to the first, and the 3rd to the 2nd, so you have to find the 1st first so you can answer the question.
You know that each person has a certain amount, and those three amounts equal $180
x (person 1) + ? + ? = 180
"The second person received $6 less than twice as much as the first", so for the 2nd amount, it is twice x minus 6
x + (2x – 6) + ? = 180
The third received $7 more than the second. So that would be twice what the first person made but plus 1, because the third person made $7 more, the second made $6 less, so that comes to a difference of $1
x + (2x – 6) + (2x +1) = 180
Now you have an equation and just have to do the math and solve for x.
For problem 2:
Stanley and Kathleen worked 69 hours. Since Stanley’s hours are based off of Kathleen’s, set her hours at x.
x + ? = 69
Stanley worked twice the hours K did, plus 6 more
x + (x + 6) = 69
Solve for x, which will give you Kathleen’s hours, then subtract that number from 69 to find Stanley’s hours.
References :
July 10th, 2010 at 10:16 am
1. If $180 was given to 3 people under those terms then with x being the 1st person:
x+(2x-6)+(2x+1)=180
5x-5=180 —-> 5x=185
x=37
1st person= $37 x—>37
2nd person= $68 2x-6—>2(37)-6—>68
3rd person= $75 2x+1—>2(37)+1—>75
2. If x is the hours Kathleen worked then:
(2x+6)+x=69
3x+6=69 —–> 3x=63
x=21
Kathleen=21 hours x—>21
Stanley= 48 hours 2x+6—>2(21)+6—>42+6—>48
It’s really not that complicated though.
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