# Homework Help: Word Problems In Algebra! Help Me Please!

1. Apr 30, 2008

### pathetic_26

1. Train A leaves a station 1/2 hour ahead of train B. The trains travel on parallel tracks. Train A travels at 25 kilometers per hour while train B travels at 35 kilometers per hour. How many hours will it take train B to overtake train A?

2. Mr. A. and Mr. B., driving their respective cars left the same place. Mr. A went north and Mr. B went south. Mr. A. drove at 50 kilometers per hour while Mr. B. at 60 kilometers per hour. In how many hours were Mr. A and Mr. B 120 kilometers apart?

3. When Prof. X drives his car to school, the trip takes one hour. When he takes cab, the trip takes 1 hour and 15 minutes. The speed of the cab is 10 kilometers per hour less than Prof. X's speed when driving. Find the distance that he travels to school.

4. Three hundred people attended a band concert. Reserved seat tickets were sold at $100 each while general admission tickets cost$60 each. If the sales totaled $26,000, how many tickets of each type were sold? 5. Mark can finish a task alone in 24 days while Andrie can do the same task in 18 days. If they work together, how long can they finish the task? 6. How many milliliters of water must be added to 240 milliliters of a 25% sulfuric acid solution to reduce the percentage of sulfuric acid in the new solution to 10%? 7. How many liters containing 8% acid should be added to 20 liters containing 60% acid in order to obtain a 40% acid solution? 8. In a NBA Basketball game, team X scored a total of 95 points. The team made five 3-point baskets. The number of the team's field goals (2 points each) is twice the number of free throws (1 point each) they made. How many free throws and how many field goals did the team make? 9. A children's playground is rectangular. The length is three times its width. If the perimeter is 504 meters, what are the dimensions of the playground? 10. The larger of two integers whose sum is 86, divided by the smaller, gives a quotient of 5 and a remainder 10. Find the numbers. 11. The sum of the digits of a two-digit number is 7. When the digits are reversed the resulting number is 27 more than the original number. Find the original number. 12. A variety of candies costing 10.50cents per kg is mixed with another variety costing 15cents per kg, to make a mixture of 12 kg that would cost 12.50cents per kg. How many kg of each variety were mixed? 13. How many liters of alcohol must be added to a mixture of 15 liters containing 6-% alcohol, to get a mixture containing 80% alcohol? 14. Mr. Smith, working as a salesman for a firm, gets a salary of$5,000 per month plus a commission of 10% on all sales above $2,000,000 per month. His total gross pay last month was$21,000. How much was his total sale last month?

15. A class will perform an experiment wherin they will need a solution of 160 cubic centimeters that is 12% hydrochloric acid. If the laboratory storeroom has only solutions containing 20% and 10% hydrochloric acid, how much of each available solution should be mixed to obtain the desired solution containing 12% hydrochloric acid?

16. Mr. Jackson invested a sum of money at 4% simple interest and another sum which is $100,000 more than the first sum, at 5%. The annual income from the two investments is$17,000. How much was Mr. Jackson's investment at each rate?

17. Mr. Sales invested $800,000 partly at %% simple interest and the rest at 10%. The amount of interest per year is the same as the amount of the interest he would receive by investing the entire$800,000 at 8.75%. How much did Mr. Sales invest at each rate?

18. A church congragation has $20,000 to be invested in a fund, part at 3% and part at 7%. If the investment at 7% earns$500 more per year than the other placement, how much is invested at each rate?

19. A man invested $35,000 partly at 15% and the rest at 18%. The total income from the investments is$5,650. Find the sum invested at each rate.

20. After her vacation in Mexico, Grace found some coins under her pillows. There were equal numbers of one peso coins and five peso coins. The number of twenty-five centavo coins was twice that of one peso coins, If the total value of the coins was P39.00, how many of each denomination did she find?

Guys, you can answer ANY NUMBER/S YOU FIND EASY AS LONG AS YOU PUT YOUR SOLUTIONS AND THE FINAL ANSWER...

I GIVE MY SINCEREST APPRECIATION TO THOSE WHO HAVE THE TIME TO STOP BY AND ANSWER THESE...THANKS SO MUCH!

ONCE AGAIN, THANK YOU! GOOD LUCK! GOD BLESS!

2. Apr 30, 2008

### danago

Nobody is just going to do your homework for you. These forums are for asking for help after you have attempted the problem.

3. Apr 30, 2008

### pathetic_26

Of course I tried to solve it but I just couldn't get the hang of it. I got some of the numbers but the rest are just so hard! I just posted it as a whole. I'm not obligating you to answer it all, I was just asking for help. I don't know what to do.

4. Apr 30, 2008

### Gokul43201

Staff Emeritus
Show us what you have tried on any problem, and then we'll help you with it.

5. Apr 30, 2008

### pathetic_26

All I know are:

11. 2+5=7, in reverse, 25 and 52 thus, resulting in 52-25=27..

18. 3x+7(500)=20,000
3x+3,500=20,000
3x=20,000-3,500
3x=16,500
3x/3=16,500/3
x=5,500

7%x500=3,500
3%x5,500=16,500

3,500+16500=20,000...

20. x=6; y=6
x+5y+2x/4=39
6+5(6)+2(6)/4=39
6+30+12/4=39
6+30+3=39
39=39..
so in conclusion, Grace had 6 pcs. of 5peso coins, 6 pcs. of 1peso coins and 12 pcs. of twenty-five cents.

I said it once, and I'll say it again, I tried to answer them!!! All I know are those three problems. The rest are just hard. And besides, I wouldn't be asking for help if I don't find it hard. I just put them as a whole. Once again, I'm NOT obligating you to answer it ALL! It's not compulsory. It's voluntary. I know some and I don't know some math. You can't expect me to be a genius. That's why I was asking for help in the first place.

6. May 2, 2008

### Tom Mattson

Staff Emeritus
Then show us what you tried.

7. May 2, 2008

### symbolipoint

Let me help only for #11.

Assign arbitrarily u = the units digit and t = the tens digit.
The original number is represented like, "tu", but understand that here, "tu" spells a number and
multiplication is NOT implied between u and t.

The sume of the digits is 7; therefore, t + u =7 [first equation].

The reversed number looks like "ut", and the meaning of this based on place value is:
u*10 + t = 'reversed digit number'
and then you are given that u*10 + t = 7 + 27 [second equation]

Now, you only have the simpler algebraic steps based on First and Second equations,
t + u =7
u*10 + t = 7 + 27
Two equations and two variables.

8. May 2, 2008

### Gokul43201

Staff Emeritus
This is not correct. The resulting number (10u+t) is 27 more than the original number (u+10t).

That makes the second equation: 10u+t=u+10t+27

9. May 2, 2008

### symbolipoint

understood.

10. May 2, 2008

### viet_jon

lol....wth?

what good is it if someone does your homework for you?

11. May 3, 2008

### pathetic_26

I've been thinking what you all said to me, and of course, I have to answer them first myself then ask for your help if there are any mistakes in my homework. I huess what I did before was pretty unfair to all and also on my part. So I'm sorry. I'm not so sure about my answers but here are some I managed to answer. I really need your help...please help me out..

12. A variety of candies costing 10.50cents per kg is mixed with another variety costing 15cents per kg, to make a mixture of 12 kg that would cost 12.50cents per kg. How many kg of each variety were mixed?

It's either..
solution A:

10.5x+15x=12(12.5)
25.5x=150
x=5.88 or 6 kilogram each

or

solution B:

12.5=(1*15+12x)/(1+x)
12.5+12.5x=15+12x
.5x=2.5
x=5kg of the 12c group for every 1kg of the 15c group.

12=x+y, where x=kg of 12c group and y=kg of the 15c group

12=y+5y
12=6y
y=2 kg of the 15c group

=x(y)
=5(2)
=10kg of the 12c group

6. How many milliliters of water must be added to 240 milliliters of a 25% sulfuric acid solution to reduce the percentage of sulfuric acid in the new solution to 10%?

240ml=75%water+25%sulfuric acid
240ml=180mlwater+60ml s. acid

If 60ml s. acid=10% then 60(10)=600ml

600ml-60ml s. acid-180ml water

2. Mr. A. and Mr. B., driving their respective cars left the same place. Mr. A went north and Mr. B went south. Mr. A. drove at 50 kilometers per hour while Mr. B. at 60 kilometers per hour. In how many hours were Mr. A and Mr. B 120 kilometers apart?

50x+60x=120
110x=120
x=1.09 or 1hr. 5 mins. amd 24 sec.s apart

1. Train A leaves a station 1/2 hour ahead of train B. The trains travel on parallel tracks. Train A travels at 25 kilometers per hour while train B travels at 35 kilometers per hour. How many hours will it take train B to overtake train A?

12.5kms
12.5kms+25/hr.x, where x<35kms/hr x
12.5<10x 1.25<x
Train B should travel > than 1.25hrs.=1 hr. 15mins to overtake train A

15. A class will perform an experiment wherin they will need a solution of 160 cubic centimeters that is 12% hydrochloric acid. If the laboratory storeroom has only solutions containing 20% and 10% hydrochloric acid, how much of each available solution should be mixed to obtain the desired solution containing 12% hydrochloric acid?

x60 cubic cm.3
=12% HCL+88%water
10%x+20%x=12%(120 cubic cm)
30%x=19.2cubic cm.
x=6.4
y=2x(12.8)
=64 cubic cm. each

7. How many liters containing 8% acid should be added to 20 liters containing 60% acid in order to obtain a 40% acid solution?

8%+60%
68%=20L
L=3.4liters

17. Mr. Sales invested $800,000 partly at 5% simple interest and the rest at 10%. The amount of interest per year is the same as the amount of the interest he would receive by investing the entire$800,000 at 8.75%. How much did Mr. Sales invest at each rate?

.5+.10+8.75=800,000
9.35=800,000
x=85,561.50 was invested

5. Mark can finish a task alone in 24 days while Andrie can do the same task in 18 days. If they work together, how long can they finish the task?

it's either...

Solution A:

72[x/24+x/18=1]72

72x/24+72x/18=72
4x+3x=72
7x=72
x=10.28 days

or

Solution B:

x+1.33x=24
2.33x=24
x=10.30days or 10days 7hrs. and 12mins.

8. In a NBA Basketball game, team X scored a total of 95 points. The team made five 3-point baskets. The number of the team's field goals (2 points each) is twice the number of free throws (1 point each) they made. How many free throws and how many field goals did the team make?

y=2z
x(3pts.+y(2pts.+z)(1pt.)=95
5(3)+2(2z+z)=95
15z=95-15
z=16 free throws

since y=2z
=2(16)
y=32 field goals

12. May 4, 2008

### Dr Zoidburg

Question One:
Train B travels 10km/hr faster than train A. Thus it's speed, relative to A, is 10km/hr.
Train A leaves 1/2 hour earlier meaning, at 25km/hr, it's 12.5km ahead.

So how long will it take train B, moving at a relative speed of 10km/hr, to travel 12.5km?

13. May 4, 2008

### rocomath

What book are you getting these problems from?

14. May 5, 2008

### BrendanH

Pathetic_26!!!!! Are You Simple?! Check Your Private Messages!