I think this is going to help you understand the concept and hope that the answer is correct. Thanks for understanding.
When simplifying an expression, you collect and simplify all the like terms. Since 8x and -12 aren’t like terms, you can’t substract 8-12
Let's have a variable for each rate
x = account 1 (2.5% rate of interest)
y = account 2 (8% rate of interest)
The formulas we need are:
0.025x + 0.08y = 830 (amount of interest paid)
x + y = 20 000 (combined amount invested)
To solve we will use substitution (isolate for one variable and plugging into the other formula):
x + y = 20 000
x = 20 000-y
0.025x + 0.08y = 830
0.025(20 000-y) + 0.08y = 830
500-0.025y+0.08y=830
500+0.055y=830
0.055y=330
y=6000
Now that we know y (the 2nd account) = $6000 we need to find x. We do this by using the previous formula.
x = 20 000-y
x=20 000 - 6000
x=14000
She invested $14 000 at a 2.5% interest rate and $6 000 at a 8% interest rate.
*Notes:
the percentages were converted into decimal form
you check your answer by plugging the numbers back into the 2 formulas we made
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18x/18 = 2/3 • 18
Flip reciprocal of 18 which is 1/18 so it would be 2/3 • 1/18 the 2 and 18 can be simplified when cross multiples so it would then be 1/3 • 1/9 which is x=1/27
