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ok do you have an example?
These are generally specific to the word problem, and probably best learned by example
A $6000 investment was $12- less than a $10000 investment at 1% less interest. what are the two rates
that should be $120
hmmm, is that the exact problem?
what should be $120?
and is it after one year?
that is how much less the interest earned is on $6000
yes annual interest
ok got it
so the amount of interest earned in a year is .% x the investment
so for the first part of the word problem we know this: 1. 6000 * x = 10000 * y - 120
that is, 6000 * the rate of interest for the first amount/rate is 120 less than the 10000 amount times its rate of interest
now, they also give you the second interest rate - for the 10000 value - is 1%
which is .01
no $10000 is one percent less than the rate for $6000
ok so they're saying after one year, the 6000 investment was 120 less than the 10000 investment, and the 10000 investment was at a 1% interest rate?
partially.. the $10000 investment is at a rate that is 1% less than the rate of the $6000 investment which yeilded $120 less.
ok, so there are two equations for two variables, x and y - with y being the % interest for the 10k investment, and x being the % interest for the second investment of 6k 1. y = x - .01 - the rate of investment for the 10k is 1 percent less than the 6k 2. 120 = 10000 *y - 6000 * x - the 10k investment at its rate yielded 120 more than the 6k at its rate
so now you need to substitute one equation into the other
how about we take the value of y from the first equation, and substitute it in place of y in the second equation
so substituting y = x - .01 into the second equation we get: 1. 120 = 10000 * (x - .01) - 6000x 2. 120 = 10000x - 100 - 6000x 3. 120 = 4000x - 100 4. 20 = 4000x 5. x = 20/4000 6. x = .005 = .5%
now given that x = .5%, and y = x - .01, we can solve for y
I messed up in step 4
120 = 4000x - 100 means 220 = 4000x
I got confused at step 2 lol
so x = 220/4000 = .055 = 5.5%
1% should equal the $120 dollars is what I was thinking
y = x - .01 means y = .055 - .01 = .045 = 4.5%
well, step 2 means that , at their annual investment rates (the amount they earn each year), we know that the 10k investment earns 120 more than the 6k investment. The amount the 10k investment earns after the first year, is 10k * rate of investment (which we're saying is "y") The mount the 6k investment earns after the first year, is 6k * rate of investment , which we're calling "x" so we know that, the amount earned by the 10k investment is 120 more than the 6k investment. so 120 = 10k*x - 6k*y
I guess I have more of a problem setting up the equation. Once I seen it I could solve it
well, practice is key with these. and honestly - that was a tricky one
took me a long time to understand what they wanted
key is to keep trying to put down equations for the things you think you know - and see if they work out. the worst thing to do is get writers block. it's hard to visualize these problems all at once, just start writing potential equations and then double check that they really do represent the word problem
Ok thanks a lot! I haven't had math in over 15 years.