## Word Problems

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
chocolateandovexeter
Posts: 1
Joined: Fri Jun 21, 2013 6:07 am
Contact:

### Word Problems

21. The number of pennies, nickels, and dimes in a bank are consecutive integers, in decreasing order. If there are n nickels, what is the value of the money in cents?
Nickels = 5(n)
Pennies= 1(n+1)
Dimes= 10(n-1)
I added them together and then I got stuck.

24-25. June and Carlos live 206 km apart. At 8AM June starts driving to Carlos' house at 60 km/h. At 10AM Carlos starts driving to June's house at 82km/h. At what time will they be 15 km apart?
24. Write an equation for the given facts. Let t be the number of hours June drives.
25. Solve the equation and answer the question.

r x t = d
June 60 x t = 60t
Carlos 82 x t+2 = 82(t+2)

I am stuck there too.

CHALLENGE PROBLEM
The total of Xanthe's, Yarrow's, and Zeke's ages is 51. Five years from now Yarrow will be the same age as Zeke is now. Six years ago, Yarrow's age was half of Xanthe's age. How old is each now?
Xanthe Now= x
Xanthe Before=???
Yarrow= y
Yarrow in 5 years= y+5=z
Zeke=z
Zeke 6 yrs ago= y-6=1/2(z-6)
Ages: x+y+z=51

I am stuck from here too.

jg.allinsymbols
Posts: 72
Joined: Sat Dec 29, 2012 2:42 am
Contact:

### Re: Word Problems

I will give just limited help on the challenge problem.

Xanthe, Yarrow, and Zeke ages now are, in same order, x, y, z.

Six Years Ago-----------------------Now-----------------------Five Years from Now
---------------------------------------x
---y-6=(x-6)/2----------------------y----------------------------y+5=z
---------------------------------------z

Putting the six-year-ago equation into a cleaner or standard form,
y-6=x/2-3
-x/2+y-6+3=0
-x/2+y-3=0
x-2y+6=0
x-2y=-6

You also have from five-year-future equation, y-z=-5

Also the sum of ages now was given as 51.

You have the system of equations:
[x+y+z=51]
[x-2y=-6]
[y-z=-5]

One way to handle that is use the second or third equation to eliminate y from the system and have two resulting equations in x and z; then solve the system for x and z, and use them to find y. That is not the only way, but I'm assuming you do not want to use matrix operations. Even so, there are other fairly simple ways to solve this system.