Word Problem: mags, calendars, and their prices

[ddee63x]

Trying to find the formula on how to calculate the following equation. 5 magazines and 1 calendar costs 24 Euros. 16 magazines and 4 calendars cost 84 euros. How much does the calendar and each magazine costs. Been out of school for over 20 years and cannot remember where to start on figuring out this formula or equation to get the result. Can someone assist?

 

[tkhunny]

Re: Word Problem

Rule #1: Name stuff.
Question #1: Name What?
Answer #1: What does it want? Name that.

M = Cost of Magazine
C = Cost of Calendar

There. After having done that, the rest is language translation. Express the problem statement in terms of these CLEAR, CONCISE, and WRITTEN definitions.

"5 magazines and 1 calendar costs 24 Euros"

5M + 1C = 24

"16 magazines and 4 calendars cost 84 euros"

16M + 4C = 84

Now the trick is to SOLVE. In this case, it's pretty easy, since C has a nice, convenient coeficient of '1'.

5M + 1C = 24 ==> C = 24 - 5M

Substitution.

16M + 4C = 84 ==> 16M + 4(24 - 5M) = 84

Can you see where to go from here?

P.S. Good call getting back at it after 20 years! Let's get to it and learn some mathematics.

 

[ddee63x]

Re: Word Problem

Thanks! I'm slowly refreshing the brain on these math equations and problem solving. However, I still haven't come to figuring out the price of the magazines and calendars. I'll work at it some more.

 

[Denis]

Re: Word Problem

TK's equation: 16M + 4(24 - 5M) = 84
I presume you're having problems with 4(24 - 5M)
That means multiply what's inside brackets by what's outside; so:
4 * 24 = 96
4 * -5M = -20M
So 4(24 - 5M) = 96 - 20M; and equation becomes: 16M + 96 - 20M = 84 ; ok?

 

[ddee63x]

Re: Word Problem

Got that part, however I was trying to figure out how to get the price of the calendar and magazine. Which is M=3 and C=9. Initially, I was trying to get those answers/results from the equation/formula.

 

[stapel]

Trying to find the formula on how to calculate the following equation. 5 magazines and 1 calendar costs 24 Euros. 16 magazines and 4 calendars cost 84 euros. How much does the calendar and each magazine costs?

Since you posted this to the "Arithemetic" category, obviously you aren't using algebra to solve this. So let's use the method my eleven-year-old uses in his curriculum:

If five magazines and one calendar cost twenty-four euros, how much would twenty magazines and four calendars cost? (Hint: Multiply.)

Given the costs for twenty magazines and four calendars, and for sixteen magazines and four calendars, how much would four magazines cost? (Hint: Subtract.)

How much then would one magazine cost? (Hint: Divide.)

How much then would five magazines cost? (Hint: Multiply.)

How much then would one calendar cost, given the cost of five magazines and one calendar, and the cost of five magazines? (Hint: Subtract.)

Have fun!

Eliz.

 

[ddee63x]

Thanks Stapel,

Need to dust off my old school books and my brain. Those simple terms you used just made it so clear. Wow!!