Question

A woman invested part of $22,000 at 5% interest and the rest at 8%. If her annual interest is $1,400, how much did she invest at 5%?

Answer 1

Given

A woman invested part of $22,000 at 5% interest and the rest at 8%.

And, her annual interest is $1,400.

To find how much did she invest at 5%.

Step-by-step explanation:

It is given that,

The principal amount is $22,000.

Let x and y be the parts of $22,000 at 5% and 8%.

Therefore,

`\begin{gathered} x+y=22000 \\ y=22000-x\text{ \_\_\_\_\_\_\lparen1\rparen} \end{gathered}`

Since the total annual interest is $1400.

Then,

`\begin{gathered} 1400=5\%* x+8\%* y \\ 1400=(5)/(100)* x+(8)/(100)*(22000-x) \\ 1400*100=5x+8*22000-8x \\ 140000=-3x+176000 \\ 3x=176000-140000 \\ 3x=36000 \\ x=(36000)/(3) \\ x=12000 \end{gathered}`

Hence, she invested $12000 at 5%.