Question

Harry has $4000 invested in two savings accounts. One account earns 6% interest per year, and the other pays 7% per year. If his total interest for the year is $264, how much is invested at 7%?

Answer 1

`color(blue)(y=$ " "2400)" "`amount invested at `7 %`

Explanation:

Let `x` be the amount invested at `6 %`

Let `y` be the amount invested at `7 %`

`x+y=4000" "`first equation
`6%*x+7%*y=264" "`second equation

also the second equation is `6/100x+7/100y=264`
and

`6x+7y=26400`

Solution by the method of substitution

`x=4000-y" "`first equation into second equation

`6x+7y=26400`

`6(4000-y)+7y=26400`

`24000-6y+7y=26400`

`color(blue)(y=2400)" "`amount invested at `7 %`

~~~~~~~~~~~~~~~~~~~~~~~

check: using the second equation
`6%*x+7%*y=264" "`second equation
`6/100(1600)+7(1/100)(2400)=264" "`second equation

`6(16)+7(24)=264`

`96+168=264`

`264=264`

correct !

God bless....I hope the explanation is useful.