Respuesta :
Answer:
She have $1133.33 in account which pays 5% annual interest and he have $1933.33 in account which pays 10% annual interest
Step-by-step explanation:
Let x be the amount she invested at 5% annual interest
She invested $800 more in 10%
So, she invested x+800 at 10% annual interest
Case 1:
Principal = x
Time = 1 year
Rate of interest = 5%
[tex]Si =\frac{P \times R \times T}{100}[/tex]
[tex]SI=\frac{x \times 5 \times 1}{100}[/tex]
[tex]SI=\frac{5}{100}x[/tex]
Case 2:
Principal = x+800
Time = 1 year
Rate of interest = 10%
[tex]Si =\frac{P \times R \times T}{100}[/tex]
[tex]SI=\frac{(x+800) \times 10 \times 1}{100}[/tex]
[tex]SI=\frac{10}{100}(x+800)[/tex]
Interest = Amount - principal = 880+1.1x-x=880+0.1x
Her total interest for a year is $250
So, [tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]
[tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]
[tex]\frac{5}{100}x+\frac{10}{100}x+80=250[/tex]
[tex]\frac{15}{100}x+80=250[/tex]
[tex]\frac{15}{100}x=250-80[/tex]
[tex]x=170 \times \frac{100}{15}[/tex]
[tex]x=1133.33[/tex]
So the amount she invested at 5% annual interest is $1133.33
She invested at 10% annual interest=x+800=1133.33+800=1933.33
Hence she have $1133.33 in account which pays 5% annual interest and he have $1933.33 in account which pays 10% annual interest
The amount she has in the account that an annual interest of 5% is $3400.
The amount she has in the account that an annual interest of 10% is $4,200.
What is the system of linear equations that represent the question?
x - y = $800 equation 1
0.1x + 0.05y = $250 equation 2
Where:
- x = amout invested in the account that earns a 10% interest
- y = amout invested in the account that earns a 5% interest
How much was invested in the account that earns a 5% interest?
Multiply equation 1 by 0.1
0.1x - 0.1y = 80 equation 3
Subtract equation 3 from equation 2
0.05y = 170
Divide both sides by 0.05
y = $3,400
How much was invested in the account that earns a 5% interest?
Substitute for y in equation 1
x - 3400 = 800
x = 3400 + 800
x = $4,200
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
