Word problems: fractions, tickets sold, driving time, etc

[Zone]

Hi, ok at the risk of sounding dumb here, I really need some help. I'm not asking for the answer, just how i go about getting it. I've seen a few of these in my sisters college algebra book, I think it's a refresher on the subject.

1. Melissa recently won an election by receiving 6390 votes. If this total was 2/3 of the total votes cast, how many votes were cast?

2. 400 tickets were sold for a school play. General admission tickets were $4, and student tickets were $3. If the total ticket sales were $1323, how many student tickets were sold?

3 Katy leaves City A for City B at 6 A.M., driving at 53 mi/h. At 7 A.M., Jensen leaves City B for City A, driving at 64 mi/h along the same route. If the cities are 638 mi apart, at what time (P.M.) will they meet?

4) And last one, -3(3x+3)=-5(2x-1)

In simple terms please (not rly a joke) lol. thanks

Zone

 

[jonboy]

Re: Word problem help

Hello Zone!

1. Melissa recently won an election by receiving 6390 votes. If this total was 2/3 of the total votes cast, how many votes were cast?

Let the total votes be \(\displaystyle x\). So solve for \(\displaystyle x\):\(\displaystyle \L \;\frac{2}{3}x\,=\,6390\)

2. 400 tickets were sold for a school play. General admission tickets were $4, and student tickets were $3. If the total ticket sales were $1323, how many student tickets were sold?

Let \(\displaystyle g\) be the number of general admission tickets. Let \(\displaystyle s\) be the number of student ticket.

Solve the system:

\(\displaystyle \L \;s\,+\,g\,=\,400\)
\(\displaystyle \L \;4g\,+\,3s\,=\,1323\)

3 Katy leaves City A for City B at 6 A.M., driving at 53 mi/h. At 7 A.M., Jensen leaves City B for City A, driving at 64 mi/h along the same route. If the cities are 638 mi apart, at what time (P.M.) will they meet?

Both travel the same distance 638 miles, \(\displaystyle d\). We know both rates, \(\displaystyle r\). So we can set up two equation using \(\displaystyle d\,=\,rt\).

\(\displaystyle \L \;638\,=\,53(t)\)
\(\displaystyle \L \;638\,=\,64(t)\)

Since the distances are the same, just solve for \(\displaystyle t\):\(\displaystyle \L \;53t\,=\,64t\)

4) And last one, -3(3x+3)=-5(2x-1)

Use the distributive property and then it's a regular problem.

\(\displaystyle \,-\,3(3x\,+\,3)\,=\,-3\,\cdot\,3x\,-\,3\,\cdot\,3\)

\(\displaystyle \,-\,5(2x\,-\,2)\,=\,-5\,\cdot\,2x\,-\,5\,\cdot\,-\,2\)

Remember to do all multiplication first. Then just solve for \(\displaystyle x\).

 

[Mrspi]

Re: Word problem help

3 Katy leaves City A for City B at 6 A.M., driving at 53 mi/h. At 7 A.M., Jensen leaves City B for City A, driving at 64 mi/h along the same route. If the cities are 638 mi apart, at what time (P.M.) will they meet?

Both travel the same distance 638 miles, \(\displaystyle d\). We know both rates, \(\displaystyle r\). So we can set up two equation using \(\displaystyle d\,=\,rt\).

\(\displaystyle \L \;638\,=\,53(t)\)
\(\displaystyle \L \;638\,=\,64(t)\)

Since the distances are the same, just solve for \(\displaystyle t\):\(\displaystyle \L \;53t\,=\,64t\)

Sorry, jonboy. I think you missed the boat on this one.....the equation you've proposed would give a solution of t = 0......

They do NOT each travel the whole 638 miles. One leaves from city A and one leaves from city B; they're traveling toward each other. By the time they meet, the distances they have traveled will add up to 638 miles.

They don't travel for the same amount of time, either. Katy leaves at 6 a.m., and Jensen leaves one hour later, at 7 a.m.

If t = number of hours traveled by Katy, then
t - 1 = number of hours traveled by Jensen.

Katy travels at 53 mph for t hours. Distance = rate * time, so the distance Katy travels is 53*t miles.

Jensen travels at 64 mph for (t - 1) hours. The distance Jensen travels is 64*(t - 1) miles.


A--------Katy---------->Meet point<-------------Jensen------------B
A<----------------------------638miles------------------------------>B

53t + 64(t - 1) = 638

NOW.....solve that for t, the number of hours Katy travels by the time they meet. Add that number of hours to Katy's departure time of 6 a.m. to find the TIME at which they will meet.

 

[jonboy]

Oh ok. Thanks for the correct Mrspi and I'm glad I learned something today.

 

[morson]

Oh ok. Thanks for the correct Mrspi and I'm glad I learned something today.

Good attitude man.