dave13 wrote:
hey Mike
these word problems with variables drive me insane
here is my solution,
let number x of the trees in the orchard each yielded 10 bushel of apples BE 10X
Let the total number be Y
total number 350
10x+y = 350
10x= 350-y (divide both parts by 10)
x = 35-y
so I where am I wrong ?
can you advice some materials for word problems ?
Dear
dave13,
I'm happy to respond.
Point #1: My friend, in word problems, each word has to be regarded with the same precision that we use on numbers in math. Everything about math is precision, both the words and the numbers. Here is the prompt again:
The harvest yield from a certain apple orchard was 350 bushels of apples. If x of the trees in the orchard each yielded 10 bushel of apples, what fraction of the harvest yield was from these x trees?I think you did not read the prompt question carefully. It was asking for a
fraction, for a part over whole. It was NOT asking you to solve for x. If you go looking for something other than what the question asks, you will not be successful on that question.
Point #2: don't introduce new variables when you don't have to. You can introduce a variable for a quantity for which you are going to solve, but don't introduce variables for extra pieces of the problem. Think about it. If the bushels from the x trees is 10x bushels, and the total number of bushels is 350, then if we needed it, the number of bushels from the remaining trees would be (350 - 10x). No need for a new variable. Be very stingy with introducing variables: don't introduce a new one unless you absolutely have to.
Point #3: when you introduce new variables, also strive for precision. Here's what you wrote:
Let the total number be Y
total number 350 You have two different "
total numbers" specified there, and it's not clear their referents:
total number of what?? It's not clear to me that you yourself are 100% clear on what the Y is, what the 350 is, and how they are different even though they are "
total numbers."
One piece of advice is to be as precise as possible in every step. Read the prompt slowly, maybe two or three times, to double-check that you understand exactly what it is and isn't asking. Make sure every variable you use in your solution is identified with surgical accuracy.
A whole other category of advice I am going to give is as follows: research and practice mindfulness. Mindfulness is a set of practices that will slow you down, allow you to release stress, and make you better able to focus on exactly what is in front of your face. A friend of mine offers these services:
Mindful Test TakingThose skills will help you a great deal on math, and they also will make you happier overall.
Does all this make sense?
Mike