Question

mark invests 8000 in an account that pays 12% interest and 2000 in one that pays 8%. if he leaves the money in the accounts for the same length of time, how long must he leave it to gain 5600 in interest​

Answer 1

mark must leave it for 5.5 months or 5 and half moths to gain 5600 in interest​ .

Explanation:

Here we have , mark invests 8000 in an account that pays 12% interest and 2000 in one that pays 8%. if he leaves the money in the accounts for the same length of time, We need to find how long must he leave it to gain 5600 in interest​ . Let's find out:

Let mark invests 8000 in an account that pays 12% interest and 2000 in one that pays 8% for time x months , So total interest gain is 5600 i.e.

⇒
`(8000(12))/(100)(x) +(2000(8))/(100)(x) =5600`

⇒
`(8000(12)+2000(8))/(100)(x) =5600`

⇒
`(80(12)+20(8))(x) =5600`

⇒
`(960+160)(x) =5600`

⇒
`(1020)(x) =5600`

⇒
`x =(5600)/(1020)`

⇒
`x =5.5`

Therefore , mark must leave it for 5.5 months or 5 and half moths to gain 5600 in interest​ .