Interest math problem

Question

Morgan invested $4,200 into two accounts. One account paid 4% interest and the other paid 7.5% interest. She earned 7%interest on the total investment. How much money did she put in each account?

Answer 1

if she earned 7% on the total investment, she earned .07 x 4200 = $294 (I assume one year invested!)

So, let a = the fraction of money at 4% and b = the fraction of money at 7.5%

Then 4200a(1.04) + 4200b(1.075) = 4494 (The original money + $294)

and a + b = 1 the same two equations then simplify as follows

4368a + 4515 = 4494

a + b = 1 when solved together you get a = .143 and b = .857

So (.143)4200 = $600.60 was invested at 4% and .857(4200) = $3599.40 was invested at 7.5%