jen invested $7500 in two bank accounts, one paying 4% simple interest, and other paying 6%, if her annual interest from the two accounts is $420, how much did she invest at each bank?

Question

whpalmer4 · Answer

We use the formula $$I = Prt$$to find simple interest.  Here we'll have $r = 0.04$ or $r = 0.06$, and $t = 1$ because we only need 1 year's worth of interest.

We know that she invested $7500 in two accounts, call the amounts $P_1,P_2$ respectively.  The interest on the two accounts will be:
$$I_1=P_1*0.04*1$$$$I_2=P_2*0.06*1$$$$I_1+I_2=420$$substituting in our expressions for the interest:$$0.04P_1+0.06P_2 = 420$$$$P_1+P_2=7500$$

That's a system that can be easily solved by substitution or elimination.

whpalmer4 · Answer

I would multiply the equation with the decimals in it by 100, to get rid of the decimals.  Then solve the other equation for $P_1$ in terms of $P_2$, and substitute it into the equation we just multiplied by 100.  Then you'll have an equation just in terms of one variable. Solve it, then use the value you found to find the other value with the $P_1+P_2=7500$ equation.

Finally, check your work: multiply your value for $P_1$ by 0.04. Multiply your value for $P_2$ by 0.06.  Verify that the two numbers add up to 420.  Then make sure that $P_1+P_2=7500$.  Your solution must work in both equations to be valid.