$5,000 is invested at 3% interest. how much money must be invested at 5% interest so that the total interest from the two investments is $275 after one year?

He must invest $ 2500 at 5% interest.

Step-by-step explanation:

Given,

$ 5,000 is invested at 3% interest,

So, the profit after one year on $ 5000 = 3% of 5000

= 0.03 × 5000

= $ 150

Now, let x be the amount invested at 5%,

So, the profit after one year on x dollars = 5 % of x

= 0.05x

Thus, the total profit in both investment,

P = 150 + 0.05x

According to the question,

P = $ 275

⇒ 150 + 0.05x = 275

⇒ 0.05x = 125 ( subtracting 150 on both sides )

⇒ x = 2500 ( Dividing both sides by 0.05 )

Hence, he must invest $ 2,500 at 5% interest.