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?

The amount invested at 4% was $600

The amount invested at 7.5%  was $3,600

Step-by-step explanation:

Let

x ----> the amount invested at 4%

$4,200-x -----> amount invested at 7.5%

we know that

The total interest earned is equal to the interest earned by the amount invested at 4% plus the interest earned by the amount invested at 7.5%

Remember that

so

The linear equation that represent this situation is

Solve for x

therefore

The amount invested at 4% was $600

The amount invested at 7.5%  was $3,600

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x