Kathy works two part-time jobs for a total of 26 hours a week. Job A pays [tex]\$6.50[/tex] per hour, and Job B pays [tex]\$6.60[/tex] per hour. How many hours did she work at each job in the week that she made [tex]\$170.00[/tex]? (Round to two decimal places if necessary.)

Let [tex]$x$[/tex] be the number of hours Kathy worked at job A (which pays \[tex]$6.50 per hour) and $[/tex]y[tex]$ be the number of hours she worked at job B (which pays \$[/tex]6.60 per hour). We are given:

1. The total number of hours worked per week is
[tex]$$x + y = 26.$$[/tex]

2. The total earnings for the week is
[tex]$$6.50x + 6.60y = 170.$$[/tex]

Step 1. Express [tex]$y$[/tex] in terms of [tex]$x$[/tex]:

From the first equation, we have
[tex]$$y = 26 - x.$$[/tex]

Step 2. Substitute [tex]$y$[/tex] into the earnings equation:

Replace [tex]$y$[/tex] in the second equation:
[tex]$$6.50x + 6.60(26 - x) = 170.$$[/tex]

Step 3. Simplify and solve for [tex]$x$[/tex]:

Distribute [tex]$6.60$[/tex]:
[tex]$$6.50x + 6.60 \times 26 - 6.60x = 170.$$[/tex]

Calculate [tex]$6.60 \times 26$[/tex]:
[tex]$$6.60 \times 26 = 171.6,$$[/tex]
so the equation becomes:
[tex]$$6.50x + 171.6 - 6.60x = 170.$$[/tex]

Combine like terms by subtracting [tex]$6.60x$[/tex] from [tex]$6.50x$[/tex]:
[tex]$$(6.50 - 6.60)x + 171.6 = 170,$$[/tex]
[tex]$$-0.10x + 171.6 = 170.$$[/tex]

Subtract [tex]$171.6$[/tex] from both sides:
[tex]$$-0.10x = 170 - 171.6,$$[/tex]
[tex]$$-0.10x = -1.6.$$[/tex]

Divide both sides by [tex]$-0.10$[/tex]:
[tex]$$x = \frac{-1.6}{-0.10} = 16.$$[/tex]

This means Kathy worked [tex]$16$[/tex] hours at job A.

Step 4. Find [tex]$y$[/tex]:

Using [tex]$y = 26 - x$[/tex]:
[tex]$$y = 26 - 16 = 10.$$[/tex]

So, Kathy worked [tex]$10$[/tex] hours at job B.

Final Answer:

Kathy worked [tex]$\boxed{16}$[/tex] hours at job A and [tex]$\boxed{10}$[/tex] hours at job B.