Question

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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 1. x + y = 4,000 and 10x + 6y = 340 2. x + y = 4,000 and 0.06x + 0.1y = 340 3. x + y = 340 and 0.1x + 0.06y = 4,000 4. x + y = 4,000 and 0.1x + 0.06y = 340. The amount Lisa invested at the rate of 10% is $1,000 or $1,500 or $2,500 or $3,500. and the amount she invested at the rate of 6% is $500 or $1,500 or $2,500 or $3,000.

Answer 1

Answer: she invested $2500 at the rate of 10%.

she invested $1500 at the rate of 6%.

Explanation:

Lisa invests $x in bond A and $y in bond B.

Lisa invests $4,000 in two types of bonds, bond A and bond B. This means that

x + y = 4000

Bond A offers a 10% return, and bond B offers a 6% return. Therefore,

Interest on bond A is 0.1x

Interest on bond B is 0.06y

Her total return on the investment is $340. It means that

0.1x + 0.06y = 340

Therefore, The system of linear equations defining the situation is

x + y = 4000

0.1x + 0.06y = 340 - - - - - - - - - - -1

Substituting x = 4000 - y into equation 1, it becomes

0.1(4000 - y) + 0.06y = 340

400 - 0.1y + 0.06y = 340

- 0.1y + 0.06y = 340 - 400

- 0.04y = - 60

y = - 60/ - 0.04

y = 1500

x = 4000 - 1500

x = 2500