Question

Help please. I'm seriously just clueless when it comes to math

Answer 1

Given:

The investment amount = $ 22954 part at 7% and rest at 5 %.

The interest earned from the amount invested at 7 % exceeds the interest earned from the amount invested at 5 % by $642.46

To find:

We need to find the investment amount at each rate.

Step-by-step explanation:

Let x be the investment amount at an interest rate of 7%

Let y be the investment amount at an interest rate of 5%

`x+y=22954`

`x=22954-y`

The interest earned from $22954-y at 7 % is

`=7\text{ \% of (22954}-y)`

`=(7)/(100)*(22954-y)`
`=1606.78-0.07y`

The interest earned from $22954-y at 7 % is $1606.78-0.07y.

The interest earned from y at 5 % is

`=5\text{ \% of y}`
`=(5)/(100)y`

`=0.05y`

The interest earned from y at 5 % is 0.05y.

We can write the following equation from the given statement.

`1606.78-0.07y=0.05y+642.46`

`1606.78-642.46=0.05y+0.07y`

`964.32=0.12y`

Dividing both sides by 0.12, we get

`(964.32)/(0.12)=(0.12y)/(0.12)`
`8036=y`

Substitute y=8036 in x=22954-y, we get

`x=22954-8036`
`x=14918`

Final answer:

The amount invested at an interest rate of 7% is $14,918

The amount invested at an interest rate of 5% is $8036.