Dillon plans to invest $16,000 part at 4% simple interest and the rest at 5% simple interest what is the most he can invest at 4% and still be guaranteed at least 700 per year

The simple interest formula is P * r * t = I, where P is the initial investment, r is the interest rate in decimal form, t is the time in years. This problem would be best solved by making a table, one row for account 1 and one row for account 2 with the formula along the top:

P * r * t = I

acct 1

acct 2

First let's fill in our years. The words "per year" were used, so the time in each row is a 1:

P * r * t = I

acct 1 1

acct 2 1

Now let's fill in the interest rates as decimals:

P * r * t = I

acct 1 .04 1

acct 2 .05 1

Now for the principle amount. If all we have to invest is 16000 and we put x into one account, then all we have left to put into the other account is what's left after taking x out of 16000, or 16000 - x.

P * r * t = I

acct 1 x .04 1

acct 2 16000 - x .05 1

The formula tells us that we multiply the P times the r times the t to get I, so lets do that. Multiply straight across the top to get an interest of .04x. Multiply straight across the bottom to get an interest of .05(16000 - x) which, after distributing, is 800 - .05x:

P * r * t = I

acct 1 x .04 1 = .04x

acct 2 16000-x .05 1 = 800 - .05x

We need the amount of interest that we earn from both of these accounts to equal 700, so add the last column and set it equal to 700:

.04x + 800 - .05x = 700. Combine like terms to get

-.01x = -100 so

x = 10,000

That means that the account which has an interest rate of 4% can have 10,000 in it while the other account has 6,000 in it.