mark must leave it for 5.5 months or 5 and half moths to gain 5600 in interest .
Step-by-step 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.
⇒ [tex]\frac{8000(12)}{100}(x) +\frac{2000(8)}{100}(x) =5600[/tex]
⇒ [tex]\frac{8000(12)+2000(8)}{100}(x) =5600[/tex]
⇒ [tex](80(12)+20(8))(x) =5600[/tex]
⇒ [tex](960+160)(x) =5600[/tex]
⇒ [tex](1020)(x) =5600[/tex]
⇒ [tex]x =\frac{5600}{1020}[/tex]
⇒ [tex]x =5.5[/tex]
Therefore , mark must leave it for 5.5 months or 5 and half moths to gain 5600 in interest .
