Answer:
13. 36 hours
14. see below for explanation
Step-by-step explanation:
13. For "w" hours of work, David's assets (in dollars) relative to Fatima's starting value will be ...
54.00 + 8.25w
Meanwhile, Fatima's assets relative to her starting value will be ...
9.75w
These values will be equal when ...
54.00 +8.25w = 9.75w
54.00 = 1.50w
54.00/1.50 = w = 36
After David and Fatima both work 36 hours, they will both have the same amount of money.
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14. You check a solution to an equation by substituting the solution value(s) for the variable(s) in the equation and doing the arithmetic. If the equation reduces to a true statement, the solution is correct.
<u>Example</u>:
f(x) = 2x +5
g(x) = 3x
A table of ordered pairs for f(x) might be ...
(x, f(x)) = {(4, 13), (5, 15), (6, 17)}
and a similar table of ordered pairs for g(x) might be ...
(x, g(x)) = {(4, 12), (5, 15), (6, 18)}
By comparing y-values we can see that f(x) = g(x) = 15 when x = 5. This is our solution found by using a table.
To check the answer, we can put x=5 into the equation ...
2x +5 = 3x
2·5 +5 = 3·5 . . . . substitute the value of x for the variable
10 +5 = 15 . . . . . . simplify a bit
15 = 15 . . . . . . a true statement; the answer checks OK
