Problems involving simultaneous equations (1 Viewer)

egz

New Member
My first post on this forum and the forum looks nice.
Anyway, I have problems with trying to pull out key points from a question when its presented in a realistic scenario and my homework currently needs me to do this to solve the questions. I ragequit after the second attempt but here are the questions:

Q3) Tickets to a concert cost $5 for children and$14 for adults. Altogether, 650 people attended the concert and ticket sales totalled $5828. Let 'a' stand for the number of adults and 'c' stand for the number of children. Solve the questions simultaneously to find the number of children that attended the concerts. Q4) Tracy bought a total of 17 DVDs and CDs. Each DVD cost her$25 and each CD cost $18. Altogether Tracy spent$390. How many DVDs did she buy?

Help will be greatly appreciated.

OT: Is there a way to add a signature on this forum?

Last edited:

fan96

617 pages
The key is to analyse the sentences and turn them into math.

4) Let $\bg_white D$ denote the number of DVD's and $\bg_white C$ the number of CD's.

Tracy bought a total of 17 DVDs and CDs
This means that $\bg_white C + D = 17$.

Each DVD cost her $25 and each CD cost$18. Altogether Tracy spent $390. She paid$25 for each DVD and $18 for each CD, and spent$390 total. That implies that $\bg_white 25D + 18C = 390$.

$\bg_white \begin{cases}18C + 25D &= 390\\ \phantom{18}C + \phantom{25}D &= 17 \end{cases}$

Rearrange the second equation:

$\bg_white \begin{cases} 18C + 25D &= 390 \\ \phantom{18C+25}C &= 17 - D \end{cases}$

Substitute the second into the first to get:

$\bg_white 18(17-D) + 25D = 390$

Then just expand, rearrange and simplify to get $\bg_white D = 12$.

You might want to check your numbers for 3): http://www.wolframalpha.com/input/?i=5c+++14a+=+5828,+c+a=650

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egz

New Member
The step by step solutions for WolframAlpha costs money, thanks for the help on the other questions. I'll check them out tomorrow since it's late right now.