Set up and solve a system of equations to solve the problem. helene invested a total of $1,000 in two simple-interest bank accounts. one account paid 5% annual interest; the other paid 7% annual interest. the total amount of interest she earned after 1 year was $62. find the amount invested in each account. helene invested $_ in the 5% interest account and $_ in the 7% account.

  Helene invested $400 in the 5% account and $600 in the 7% account.

Step-by-step explanation:

Let x and y represent the amounts Helene invested in the 7% and 5% accounts, respectively. Then a system of equations based on the problem statement can be ...

  x + y = 1000

  0.07x +0.05y = 62

Solving the first equation for y and substituting that into the second equation, we get ...

  y = 1000 -x . . . . . . subtract x from both sides of the first equation

  0.07x +0.05(1000 -x) = 62 . . . after substitution for y

  0.02x + 50 = 62 . . . . . . . . . simplify

  0.02x = 12 . . . . . . . . . . . . . . subtract 50

  12/0.02 = x = 600 . . . . . . . .divide by the coefficient of x

  y = 1000 -x = 1000 -600

  y = 400

Helene invested $400 in the 5% account and $600 in the 7% account.

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following