Wordproblems

[awuah29]

Hi,
anyone knows how to set up those wordproblems

1.One number is 11 more than three times another. Their sum is 111. What are the numbers?


6. There are three consecutive even numbers such as twice the first is 20 more than the second . Find the numbers.


7. A carpenter needs to cut a 14 foot board into three pieces so that the second piece is twice as long as the first and the third is twice the second. How long is the shortest piece?


13 The Moutainneering Shop was owned jointly by Dave, Steven, and Pierre. Steve put up $2000 more than Dave, and Pierre owned a half interest. If the total cost of the shop was $52,000, how many did each man invest?


15. Wolfgang and Heinrich worked as electricians for $40 and 44 per hour , respectively. One month Wolfgang worked 10 hours more than Heinrich. If their total income for the month was $11,320, how many hours did each work during the month?


16.Mike and Ike each inherited a sum of money from an uncle. Mike received $800 more than Ike. Ike invested his at 8 percent and Mike invested his at 7 percent. If Mike received $ 16 a year more than Ike in interest, how much did each inherit?

[bold_n_beast]

Hi,
anyone knows how to set up those wordproblems

1.One number is 11 more than three times another. Their sum is 111. What are the numbers?

Soln: Let one number is X, then other number is 3X+11, this implies
X+3X+11 = 111
X = 25
So, Numbers are 25, 86

6. There are three consecutive even numbers such as twice the first is 20 more than the second . Find the numbers.

Soln: Let the three consective even numbers are, X-2, X, X+2. So,
2(X-2) - 20 = X
2X - 24 = X
X = 24
So Ans is: 22, 24, 26


7. A carpenter needs to cut a 14 foot board into three pieces so that the second piece is twice as long as the first and the third is twice the second. How
long is the shortest piece?

Soln:
|----|-----|---------|
A B C D
where,
AD = AB + BC + CD = 14
BC = 2*AB
CD = 2*BC = 2 * (2 * AB)

this implies AB + 2*AB + 4*AB = 14
Hence AB = 2 foot (Ans)

13 The Moutainneering Shop was owned jointly by Dave, Steven, and Pierre. Steve put up $2000 more than Dave, and Pierre owned a half interest. If the total
cost of the shop was $52,000, how many did each man invest?

Soln:

D + S + P = 52, 000
Where D = X $
S = X + 2,000
P = 52, 000 / 2 = 26, 000
=> X + X + 2000 + 26000 = 52000
X = 12000
So Ans:
D = 12000 $
S = 14000 $
P = 26000 $

15. Wolfgang and Heinrich worked as electricians for $40 and 44 per hour , respectively. One month Wolfgang worked 10 hours more than Heinrich. If their
total income for the month was $11,320, how many hours did each work during the month?

Let H worked X hours in a month, then
X*44 + (X+10)*40 = 11320
X * 11 + (X+10) * 10 = 2830
21 * X = 2730
X = 160
So H worked 160 hours and W worked 170 hours.

16.Mike and Ike each inherited a sum of money from an uncle. Mike received $800 more than Ike. Ike invested his at 8 percent and Mike invested his at 7 percent. If Mike received $ 16 a year more than Ike in interest, how much did each inherit?
Let I inherit X money. then
X*8/100 = [ (X+800) * 7 / 100 ] - 16
8 * X = 7 * X + 5600 - 1600
X = 4000
so ans is Ike inherit 4000 $ and Mike Inherit 4800 $.

[bscout]

I realise that this problems were posted a long time ago but I wanted to clear the results to avoid any confusion.

I slightly disagree with the bold's results for question [15].

Let x be the numbers of hours worked by Wolfang in a month and y the numbers of hours woked by Heinrich.

x = y+10
40x+44y = 11,320

Solving the system ==> x = 140 and y = 130.

[sruthi07]

15. Wolfgang and Heinrich worked as electricians for $40 and 44 per hour , respectively. One month Wolfgang worked 10 hours more than Heinrich. If their
total income for the month was $11,320, how many hours did each work during the month?

Let H worked X hours in a month, then
X*44 + (X+10)*40 = 11320
X * 11 + (X+10) * 10 = 2830
21 * X = 2730
X = 160
2730/21= 130
So H worked 130 hours and W worked 140 hours.

16.Mike and Ike each inherited a sum of money from an uncle. Mike received $800 more than Ike. Ike invested his at 8 percent and Mike invested his at 7 percent. If Mike received $ 16 a year more than Ike in interest, how much did each inherit?
Let I inherit X money. then
X*8/100 = [ (X+800) * 7 / 100 ] - 16

8 * X = 7 * X + 5600 - 1600
X = 4000
so ans is Ike inherit 4000 $ and Mike Inherit 4800 $.

X*8/100 = [ (X+800) * 7 / 100 ] - 16

Shdnt this step be rewritten as;
[ (X+800) * 7 / 100 ]=$16 + X
OR;
in line with yours shdnt it be:
X*8/100= [ (X+800) * 7 / 100 ]-16-X ??
can u clarify??

[TargetGRE6]

13 The Moutainneering Shop was owned jointly by Dave, Steven, and Pierre. Steve put up $2000 more than Dave, and Pierre owned a half interest. If the total
cost of the shop was $52,000, how many did each man invest?

How could Pierre owned a half of interest = 52000/2 cost?

[Halking]

it seems that all correct answers is here!
that's wonderful!