you have 2 different savings accounts. for account a, the simple interest earned after 15 months is $9.25. for account b, the simple interest earned after 27 months is $21.60. if the interest rate is 3.7% for account a and 2.4% for account b, how much is the principal in each account? which account earned you the most interest the first month? explain your answer

Principal in Account A: $16.67

Principal in Account B: $33.33

Account B earned the most interest in the first month.

Step-by-step explanation:

Use the simple interest formula:

"I" represents total interest earned

"P" is principal, the starting amount

"r" is the rate of interest in decimal form. Find this by dividing percentage by 100.

"t" is the time where interest was earned

Substitute all the information you know into the equation. Then isolate "P" to find the principal. Next, use the formula to calculate the interest for 1 month.

Account A

t = 15

I = 9.25

r = 3.7%   ==> Convert to decimal: 3.7/100 = 0.037

Find principal:

I = Prt

9.25 = P(0.037)(15)

9.25 = 0.555P    <=Divide both sides by 0.555

P = 16.67

First month interest:

I = Prt

I = 16.67(0.037)(1)

I = 0.62

Account B

t = 27

I = 21.60

r = 2.4%   ==> Convert to decimal: 2.4/100 = 0.024

Find principal:

I = Prt

21.60 = P(0.024)(27)

21.60 = 0.648P    <= Divide both sides by 0.648

P = 33.33

First month interest:

I = Prt

I = 33.33(0.024)(1)

I = 0.80

The first month interest in Account B was more than in Account A.

0.80 > 0.62

Therefore, the principal in Account A is $16.67. The principal in Account B is $33.33. Account B earned the most interest in the first month.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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