An actor invests some money at 5% simple interest, and $23,000 more than 3 times the amount at 6% simple interest. The total annual interest earned from the investment is $28,290. How much did he invest at each amount? Use the 6 step method.

He invested $117,000 at 5% interests and  3*117,000 + 23000 = $374,000 at 6% interests

Step-by-step explanation:

Let's call x to the some money at 5% simple interest the actor invest. Then, he invested 3x + 23000 dollars at 6% simple interest.

At 5% simple interest, after one year he earned the following interests:

I = P*r*t

I = x*0.05

At 6% simple interest, after one year he earned the following interests:

I = (3x + 23000)*0.06 = 0.18x + 1380

The total annual interest earned from the investment is $28,290, then:

0.05x + 0.18x + 1380 = 28290

x = (28290 - 1380)/0.23

x = $117,000

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.