A word problem

Another word problem was sent my way.
Todd, Chris, and Rod have 30 birds. Rod has five times as many as Todd. Todd has one fourth the number Chris has. How many birds do they each have?
The numbers in this problem are so small that I won't make any equations -- it might be QUICKER to use guess and check!

Just notice Todd has the least amount, and once you know (or guess) how many birds Todd has, then you immediately know how many Chris and Rod have. Rod will have 5 times the amount Todd has, and Chris will have four times the amount Todd has.

We will start by giving Todd 1 bird, and checking if the condition is met that the total becomes 30. Then we will give Todd 2 birds and check again.

Rod 5 10 15
Chris 4 8 12
Todd 1 2 3
Total 10 20 30

So Todd has 3 birds, Chris has 12, and Rod has 15.

I'm guessing this might be a problem from algebra course, and that the author/teacher intends algebra to be used. But I would say that use the most effective and quick method which isn't always algebra...

With algebra, you'd assign Todd to have x birds, then Chris has 4x birds and Rod has 5x birds. Add those up and let the sum be 30:

x + 4x + 5x = 30

10x = 30

x = 3.

So it's pretty quick this way too. I just chose the guess and check because the total was only 30 and so I knew it wouldn't take long.


Deborah said…
Hi Maria, I thought i'd let you know, I've posted about Math Mammoth on my blog:
Deborah said…
By the way...word problems like this one just make my mind freeze and my belly queasy! That could be why I'm such a lousy math teacher! LOL
Maria Miller said…
Oh, no need to feel queasy! We'll just take it easy. I did, didn't I? Just guess and check. Honestly, it becomes easy with some practice, because the basic ideas in these word problems are just recirculated over and over, so the problems resemble other similar ones.
lorig said…
I found your blog from another I visit. I showed my girls this word problem (they are 7 and 8). The 7 year old immediately started guess and check at one but skipped assigning 2 to x because she could already see the answer, now I know why she is bored at school. I'll check out some of the links you provided they may be very helpful to me in the coming months.
Jill said…
As a former math teacher in the middle school grades, I found it easiest and fastest to crank out the simple equations and then solve. Maybe it is just me but I enjoy these little challenges to get the cobwebs out first thing in the morning! Thanks for sharing.

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