Question

Lisa invests $4,000 in two types of bonds, bond A and bond B. Bond A offers a 10% return, and bond B offers a 6% return. Lisa invests $x in bond A and $y in bond B. Her total return on the investment is $340.
The system of linear equations defining the situation is . The amount Lisa invested at the rate of 10% is , and the amount she invested at the rate of 6% is .

Answer 1

x+y=4000....(1)
10x+6y=340*100⇒5x+3y=17000......(2)

(2)- 3*(1)⇒ 2x=5000⇒x=2500,y=4000-2500=1500

Answer 2

Answer: The amount invested at the rate of 10% is $2500 and that of 6% is $1500.

Step-by-step explanation:  Given that Lisa invests $4,000 in two types of bonds, bond A and bond B. Bond A offers a 10% return, and bond B offers a 6% return.

Lisa invests $x in bond A and $y in bond B and her total return on the investment is $340.

According to the given information, the system of linear equations can be written as

$x+y=4000~~~~~~~~~~~~~~(i)\\\\10\%\times x+6\%\times y=340\\\\\\\Rightarrow \dfrac{10}{100}x+\dfrac{6}{100}y=340\\\\\\\Rightarrow \dfrac{x}{10}+\dfrac{3x}{50}=340\\\\\\\Rightarrow \dfrac{5x+3y}{50}=340\\\\\Rightarrow 5x+3y=17000~~~~~~~~~~~~~~(ii)$

Multiplying equation (i) by 5, we have

$5x+5y=20000~~~~~~~~~~~~~~~~(iii)$

Subtracting equation (ii) from equation (iii), we get

$(5x+5y)-(5x+3y)=20000-17000\\\\\Rightarrow 2y=3000\\\\\Rightarrow y=1500,$

and from equation (i), we get

$x=4000-1500=2500.$

Thus, the system of linear equations defining the situation is

$x+y=4000\\\\5x+3y=17000,$

and

the amount Lisa invested at the rate of 10% is $2500 and the amount she invested at the rate of 6% is $1500.