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jeka94
3 years ago
5

Heather has divided ​$5400 between two​ investments, one paying 8​%, the other paying 5​%. if the return on her investment is ​$

345, how much does she have in each​ investment?
Mathematics
1 answer:
Phantasy [73]3 years ago
6 0

Answer:

$2500 at 8%.

$2900 st 5%.

Step-by-step explanation:

Let x be the amount invested at rate of 8% and y be the amount invested at the rate of 5%.

We have been given that Heather has divided ​$5400 between two​ investments. We can represent this information as:

x+y=5400...(1)

The return on her investment is ​$345.  

Earnings from the investment at 8% will be 8% of x.

Earnings from the investment at 5% will be 5% of y.

(\frac{8}{100})x+(\frac{5}{100})y=345...(2)

0.08x+0.05y=345...(2)

We will use substitution method to solve our system of equations. From equation (1) we will get,

x=5400-y

Substituting this value in equation (2) we will get,

0.08(5400-y)+0.05y=345

432-0.08y+0.05y=345

-0.08y+0.05y=345-432

-0.03y=-87

\frac{-0.03y}{-0.03}=\frac{-87}{-0.03}

y=2900  

Therefore, Heather has invested an amount of $2900 at 5%.

Let us substitute y=2900 in equation (1) to solve for x.

x+2900=5400

x+2900-2900=5400-2900

x=2500

Therefore, Heather has invested an amount of $2500 at 8%.

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