How do you set up the formula to the word problem below?

Question

rosalinda invested some of her $15000 in bonds that made 6% profit and the rest in bonds that made a 10% profit. If the profit on the 10% bonds was $1000 more than the profit on the 6% bonds, how much did Rosalinda invest in the 6% bonds?

Answer 1

Hi Dan,

 

Let's begin by writing algebraic expressions to represent the amount invested at each profit percentage:

    x = amount invested at 6% profit

    15,000 - x = remainder invested at 10% profit

 

Now let's write an equation using our algebraic expressions for the two invested amounts and the two profit percentages to express the relationship between the two profit amounts:

    Verbal Relationship:

        Profit Amount at 10% =

        Profit Amount at 6%   + $1,000

    Percent Conversion to Decimal:

        10% = 10/100 = 0.10
        6% = 6/100 = 0.06

    Algebraic Equation (our answer):

        0.10(15,000 - x) = (0.06)(x) + 1,000

 

Our algebraic equation can now be used to solve for the amount invested at 6% profit (represented by the letter "x").

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan (Romans 5:8).