Question: Betty invested some money at 15% interest. Betty also invested
more than 2 times that amount at 13%. How much is invested at each rate if Betty receives
in interest after one year? (Round to two decimal places if necessary)
Detailed Solution:
From the given problem, it is evident that there are two different investments. One investment earns 15% interest and the other investment earns 13%.
Let us say that the amount X is invested at 15% interest, amount Y is invested at 13% interest.
Since there are two variables X & Y, We need to frame two equations to solve for the two given variables.
Amount of interest earned by the amount X at 15% interest =
Amount of interest earned by the amount Y at 13% interest =
Given is the total interest earned from the two investments.
Therefore
Multiplying with 100 throughout the equation to avoid the decimals.
15x+13y=168803—->Equation 1
Given that the “Betty invested $237 more than 2 times that amount at 13%”
Therefore we can say
y= 2x+237 —->Equation 2
By using the substitution method, we can replace y as 2x +237 in Equation 1.
15x+13(2x+237)=168803
15x+26x+3081=168803
41x=168803-3081=165722
X=4042
Therefore y= 2x+237 =2(4042)+237
Y=8321
Therefore,In conclusion,the amount invested at 15% is and the amount invested at 13% interest is
.
Verification:
We can cross check the answers we got for the X =4042 and Y =8321 values.
When the values of X and Y are plugged back into the original equations, they must hold good.
Let us take up the equation1
15x+13y=166803
15(4042)+13(8321)=168803
60630+108173=168803
168803=168803.Therefore, the solutions we arrived work for the equation1
Let us cross-check with the equation2.
y=2x+237
8321=2(4042)+237
8321=8321 Therefore, the solutions we arrived work for the equation2 as well.
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