Question

jack owns 13 more shoes than half of the number of shoes jill owns. together jack & jill own 43 shoes. let x represent the number of shoes jacks owns & y represent the number of shoes jill owns.​

Answer 1

To solve the problem, two equations are formed based on the information given: x = \( \frac{1}{2}y + 13 \) and x + y = 43. By substituting the first equation into the second and solving for y, it is determined that Jill owns 20 shoes and hence Jack owns 23 shoes.

Step-by-step explanation:

The question involves setting up a system of equations to determine the number of shoes owned by Jack and Jill. We are given that Jack owns 13 more shoes than half of the number owned by Jill, and together they own 43 shoes. To express this mathematically:

Let x = the number of shoes Jack owns

Let y = the number of shoes Jill owns

We can set up the two equations as follows:

1. x = \( \frac{1}{2}y + 13 \) (Because Jack owns 13 more than half the number of Jill's shoes)
2. x + y = 43 (Because together they own 43 shoes)

To solve for x and y, we substitute the first equation into the second equation:

\( \frac{1}{2}y + 13 + y = 43 \)

Combining like terms, \( \frac{3}{2}y + 13 = 43 \)

Subtracting 13 from both sides, \( \frac{3}{2}y = 30 \)

Multiplying both sides by \( \frac{2}{3} \), we find that y = 20.

Substituting y back into the first equation:

x = \( \frac{1}{2}(20) + 13 \)

Therefore, x = 23.

So, Jack owns 23 shoes and Jill owns 20 shoes.

Answer 2

`jack = (1)/(2) (jill) + 13 \\ 43 - 13 = 30 \\ 30 / 3 = 10 \\ jack = 13 + 10 \\ jill = 10 + 10`

Jack= 23 shoes

Jill=20 shoes