Daisy invests a total of $12900 in two accounts. One account pays 9% annual interest and the other pays 8% annual interest. If the total annual interest from both accounts is $1103, how much was invested in each account? Suppose x is the amount invested at 9% and y is the amount invested at 8%. Find an answer question above using a system of linear equations of x and y. List the equations in that system.

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artwale artwale · Answer 1 · 2020-11-01T01:56:15+01:00

Answer:

The equations:

[tex]x + y = 12900\\.09x + .08y = 1103[/tex]

the value for x and y:

[tex]x = 7100\\y = 5800[/tex]

Step-by-step explanation:

invest amount = 12900

let x = amount put into the first account

let y = amount put into the second account

we know the sum of of both is 12900, thus

[tex]x + y = 12900[/tex]

We also know the sum of their annual interest rate is 1103

[tex].09x + .08y = 1103[/tex]

Thus the equations needed are

[tex]x + y = 12900[/tex] and [tex].09x + .08y = 1103[/tex]

To find the values for x and you know have all equations you need

we need to get this equation [tex].09x + .08y = 1103[/tex] to a single variable

we can do this using x or y, lets use x

we know

[tex]x + y = 12900[/tex], so

[tex]x = 12900 - y[/tex]

lets plug [tex]x = 12900 - y[/tex] into [tex].09x + .08y = 1103[/tex]

[tex].09(12900 - y) + .08y = 1103[/tex]

1161 - .09y + .08y = 1103

-.01y = -58

y = 5800

we can get x from this equation [tex]x = 12900 - y[/tex] from above

[tex]x = 12900 - 5800\\x = 7100[/tex]