Arithmetic Problems

[elin1]

How do you solve these problems?
1. Given 10 gallons of 3% alcohol, how much 9% alcohol should be added to make a 5% mixture?
2. How long does it take for sunlight to travel from the sun to the earth?
The speed of light is 3 times 10 to the power of 8. The distance between the sun and the earth is 150 million kilometers.
Solve arithmetically:
Tickets for a show are $3 for kids and $10 for adults. The auditorium holds 450 people. The sold out show raised $2750 in ticket sales. How many kid tickets were sold?

Thanks

 

[mmm4444bot]

… The speed of light is 3 times 10 to the power of 8.

I'm concerned about this value for speed, for two reasons.

Firstly, there are no units stated.

Secondly, the power of ten might be wrong. The speed of light is roughly:

3 * 10^5 kilometers per second

Exercises (1) and (3) look like algebra problems, to me. Are you in an algebra class? (They are solved similarly because they are both of the "mixture" type.)

Exercise (2) can be answered by using the following relationship that relates elapsed time, speed, and displacement of an object moving at a constant speed.

D = R * T

In words, "Distance equals Rate times Time".

Said another way, "The distance that a moving object covers during some amount of elapsed time may be expressed as the product of the object's constant speed (rate) multiplied by the amount of elapsed time."

EG: A migrating bird flies at a constant speed of 10 miles per hour. How long does it take this bird to fly 50 miles?

D = R * T

The distance is 50, and the rate is 10.

50 = 10 * T

Since we know that 5 times 10 is 50, it's clear that T = 5.

It takes the bird 5 hours to fly 50 miles at a constant speed of 10 mph.

If we are taking an algebra class, then we would "solve" the equation that we set up.

50 = 10 * T

Divide both sides of the equation by 10, in order to isolate the symbol T.

50/10 = (10 * T)/10

5 = T

Therefore, you can set up an equation for exercise (2).

OR, here's another way of approaching the same problem.

Start with the relationship D = R * T

Exercise (2) asks you for T, so solve this relationship for T by dividing both sides by R.

D/R = T

Now, we have a formula that gives us the elapsed time when we know the distance traveled and the speed.

Your exercise (2) gives you some distance traveled by light (D), and it gives you the rate of travel (R).

The units of displacement are "kilometers". IF the units given to you for the rate are "kilometers per second" (kps), then divide D by R, and you'll get the elapsed time T (in seconds).

And, IF the units on the rate are in fact kps, then, as I mentioned above, you've either been given the wrong value OR you made a typographical error.

The speed of light is about 3 * 10^5 kps.

One last thought. Since they used Scientific Notation on the rate, I'm guessing that your instructor would like to see you write 150 million kilometers in Scientific Notation lso. So, I would do the division with both values in Scientific Notation (using properties of exponents, etc.), followed by writing your answer in Scientific Notation, too.

Again, are you in an algebra class?

I'm thinking that exercises (1) and (3) should be solved algebraically, not "arithmetically".

If I typed anything that you do not understand, then please ask specific questions.

 

[elin1]

Thank you for the reply.
I have solved problem 3 algebraically but there must be a way to solve it arithmetically. How do you solve problem 1 algebraically.
No I am not in algebra class. We are trying to solve some 8th grade problems arithmetically.

I forgot to include the units for the speed of light. It is 3 times 10 to the power of 8 miles per second.

 

[Deleted member 4993]

Thank you for the reply.
I have solved problem 3 algebraically but there must be a way to solve it arithmetically. How do you solve problem 1 algebraically.
No I am not in algebra class. We are trying to solve some 8th grade problems arithmetically.

I forgot to include the units for the speed of light. It is 3 times 10 to the power of 8 miles per second.

Incorrect

If it is referring to the speed of light in vacuum in this universe, it is a constant - and it is approximately 3 * 10[sup:4n1wcz6l]8[/sup:4n1wcz6l] cm/sec.

 

[elin1]

Ok. The units were probably incorrect. Thanks for the reply any how. How do you solve the precent problem?
Thanks

 

[mmm4444bot]

… The units were probably incorrect …

Probably?

If you're not clear that they are OBVIOUSLY incorrect, after everything that's been stated in this discussion, then you might not be ready to do these exercises.

CLICK HERE TO SEE RESOURCES ON SOLVING MIXTURE-TYPE WORD PROBLEMS

If you would like more help on any of these exercises, then please show your work and ask specific questions.

 

[elin1]

Ok Thanks I guess the instructor was not so much being correct as trying to get me to use Scientific Notation

 

[elin1]

This site seems to be quite interesting. Keep it up! Thanks for the replies. I will be back soon.