You inherit $18750 but the conditions are that for the first year, the money must be invested in two stocks paying 10% and 11% interest, respectively. How much should be inbested at each rate if the total interest to be earned for the year at $1962.51? Be sure to specify what your variable stands for and to set up an algebraic equation which models the problem. then solve the equation and answer the question.

Question

You inherit $18750 but the conditions are that for the first year, the money must be invested in two stocks paying 10% and 11% interest, respectively. How much should be inbested at each rate if the total interest to be earned for the year at $1962.51? Be sure to specify what your variable stands for and to set up an algebraic equation which models the problem. then solve the equation and answer the question.

H means amount at higher interest.

.11H + .10(18750-H)=1962.71
Wouldn't that do it?

Answer 1

Yes, you are on the right track. Here's how you can continue to solve the equation:

Let's rewrite the equation using the variable H, as you mentioned:

0.11H + 0.10(18750 - H) = 1962.51

Now, let's solve this equation step by step:

Step 1: Distribute the 0.10 to both terms inside the parentheses:
0.11H + 1875 - 0.10H = 1962.51

Step 2: Combine like terms on the left side of the equation:
0.01H + 1875 = 1962.51

Step 3: Subtract 1875 from both sides to isolate the H term:
0.01H = 1962.51 - 1875
0.01H = 87.51

Step 4: Divide both sides by 0.01 to solve for H:
H = 87.51 / 0.01
H = 8751

Now that we have the value of H, we can find the amount invested at the lower interest rate by subtracting H from the total inheritance:

18750 - H = 18750 - 8751
= 9999

Therefore, the inheritance should be invested $8,751 at a higher interest rate and $9,999 at the lower interest rate in order to earn a total interest of $1962.51 for the year.