maria has 4 times as many necklaces as shelia. together , they have 25 necklaces. how many necklaces does maria have?

Question

Maria has 4 times as many necklaces as Shelia. Together, they have 25 necklaces. How many necklaces does Maria have?

Answer 1

"maria has 4 times as many necklaces as sheila". this sentence becomes an equation by using symbols instead of long strings of words. that is usually the hardest step, and the most important one, since you need to get your relationships correct in the beginning. To me, this sentence translates to M = 4S. In grade school, we are taught to look for clue words, but we can just as easily reword the problem so we see the clue words we are familiar with. Where is the equal sign found, for example? How about I say "the number of necklaces maria has IS four times as many as the number of necklaces that sheila has"? That's where I get the equation, M = 4S. The Next step: The shortening of long strings of text into a single letter is a matter of convenience. instead of "the number of necklaces maria has", why not save space and ink by writing M? As long as i know what it stands for! in this problem, names are given, so go ahead and use their initials for variables - it helps you realize what you are counting. try to imagine the people in the problem, and the items we are counting, and get a visual image. don't spend too much time sketching but give yourself a little picture to go with the problem. Finally, if you go back and look at the first equation M=4S, there are 2 unknowns. One of the first rules of algebra is - you need a unique equation for each variable present in order to solve the problem. So if we look at the equation m=4s, it only tells us that maria has 4 times as many as sheila. for all we know, maria could have 400 and sheila could have 100. so we need another equation. two equations for two unknowns, 3 for 3, and so forth. no one can ever write a word problem that gets around that. it's an algebra thing and all we can do is obey the math. So looking back at the problem, we see that M + S = 25 or in English, the number of necklaces maria has plus the number of necklaces sheila has is equal to 25........ Ok now what? we set up our equations but we have 2 separate equations and no answer.....think think think OH YEAH! SUBSTITUTION!! You see, we all get very excited when we near the end. All we have to do is look at our two equations and ask ourselves - is there a way to make one equation out of the 2 i have, where i only have one variable? Because otherwise i'm still stuck. Let's take the equation M=4S. Ready? Use the expression "4S" instead of M, and in the second equation, we can rewrite it as 4S + S = 25. Or in other words, 5S = 25. Which means that S = 25/5, or 5. Which then means that M is 4*5, or 20. Go back and read the problem using the numbers you figured out. Both equations should work. 

Answer 2

In these type of problems, Tarsha, it is helpful to let the quantity after the word "as" be equal to x (or whichever variable you choose to use). Then, we can express the other quantity in terms of x. Therefore, let the number of necklaces that Shelia has equal x. Maria has 4 times as many as Shelia, so that means she has 4x. Together, the two girls have 25 necklaces. We can now form an equation.

 

x + 4x = 25

 

You should now be able to solve this for x, Tarsha. Once you obtain x, you can determine how many Maria has by computing 4x.